The linear Cahn-Hilliard equation with an interface

Alain Miranville; Andreas Chatziafratis; Tohru Ozawa

arxiv: 2605.20130 · v1 · pith:DSZJ7C3Tnew · submitted 2026-05-19 · 🧮 math.AP · math-ph· math.CV· math.MP

The linear Cahn-Hilliard equation with an interface

Andreas Chatziafratis , Alain Miranville , Tohru Ozawa This is my paper

Pith reviewed 2026-05-20 03:17 UTC · model grok-4.3

classification 🧮 math.AP math-phmath.CVmath.MP

keywords Cahn-Hilliard equationinterface problemsFokas unified transform methodcontour integralsfourth-order PDElinearized evolution equationinitial-boundary value problems

0 comments

The pith

Contour integral formulas represent solutions to the linearized Cahn-Hilliard equation with general interface conditions at one point.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper derives explicit representations for solutions of the linear Cahn-Hilliard equation on the real line when interface conditions are imposed at the origin. The formulas take the form of contour integrals in the complex Fourier plane and cover arbitrary initial data together with fully nonhomogeneous terms. A reader would care because these expressions make it straightforward to examine regularity, decay rates, and long-time limits of the solutions. The same formulas supply a route toward well-posedness results for nonlinear versions and toward models with moving or diffuse interfaces.

Core claim

What carries the argument

Extension of the Fokas unified transform method to a fourth-order linear operator, producing contour integrals in the complex Fourier plane that encode the effect of general interface conditions at a single point.

If this is right

The formulas permit direct analysis of regularity and asymptotic behavior without solving the PDE numerically.
They supply a foundation for proving well-posedness of corresponding nonlinear Cahn-Hilliard problems.
The representations extend naturally to the study of free-boundary and diffuse-interface models.
Qualitative features such as decay rates or smoothing properties follow from contour deformation or residue calculus.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The same contour-integral technique may transfer to other fourth-order evolution equations that appear in phase-field models.
Numerical schemes that evaluate the integrals along suitable contours could be developed for practical computation of interface problems.
The method suggests a possible route to time-dependent interface locations by treating the transmission conditions as evolving parameters.

Load-bearing premise

The Fokas unified transform method extends to fourth-order operators with general interface conditions at a single point on the line.

What would settle it

Substitute the proposed contour integral expressions back into the PDE and the interface conditions and check whether they recover the equation and the prescribed jumps or transmission rules for a concrete choice of data with an independently known solution.

read the original abstract

We obtain new integral representations, expressed as contour integrals in the complex Fourier plane, for the solution of fully nonhomogeneous interface problems for the linearized Cahn-Hilliard equation with arbitrary initial data on the line and general interface conditions prescribed at the origin. Cahn-Hilliard-type models emerge in applied mathematics in connection to a spectacular variety of phenomena of mathematical physics, continuum mechanics, chemistry and biology. A novel implementation of Fokas' unified transform method is in force herein for a fourth-order operator for the first time, with particular challenges arising due to the nature and the generality of the problems under consideration. Our explicit formulae directly lend themselves to exploration of the solution's qualitative properties such as regularity and asymptotic behavior. This work is also useful in the investigation of well-posedness for nonlinear counterparts as well as in the study of free-boundary and diffuse-interface problems.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

They derive explicit contour-integral formulas for the linear Cahn-Hilliard on the line with a point interface at zero via a new Fokas extension, but the closure of the spectral system for general conditions is the part that still needs close checking.

read the letter

The paper works out new contour-integral representations for solutions of the linearized Cahn-Hilliard equation with an interface at the origin. They handle arbitrary initial data on the whole line and general interface conditions, which is the main concrete output. The approach extends the Fokas unified transform to a fourth-order operator for the first time, splitting the line into two half-lines, writing global relations, and solving for the unknown interface traces in the complex plane. That produces the claimed formulas, and the abstract is right that these can be used to read off regularity or large-time behavior without solving the PDE numerically. The work is also positioned as a stepping stone toward nonlinear or free-boundary versions, which makes sense given how Cahn-Hilliard models appear in applications. The derivations look formally consistent on the page, and they cite the relevant prior Fokas literature without obvious gaps. The soft spot is exactly the algebraic closure step the stress-test note flags. For fourth-order problems you end up with more unknown spectral functions than in the usual second-order case, and the matrix that relates them comes from the jump conditions evaluated at complex k. The paper asserts that the system can be solved throughout the relevant sectors where the exponentials decay, but I would want to see the explicit determinant or the solved expressions rather than just the statement that it works for arbitrary conditions. If that matrix is invertible without extra hidden identities, the result stands; if not, the formulas only hold under restrictions not stated up front. The evidence in the manuscript is the derivation itself, so the claim is only as strong as that calculation. This is for readers already working on interface problems or on the Fokas method in higher-order PDEs. Someone looking for explicit solution formulas in one dimension would find it directly useful. It is worth sending to a serious referee because the method is new for this setting and the output is concrete, even though the invertibility detail will probably need tightening in revision.

Referee Report

0 major / 3 minor

Summary. The manuscript claims to obtain new integral representations, expressed as contour integrals in the complex Fourier plane, for the solution of fully nonhomogeneous interface problems for the linearized Cahn-Hilliard equation with arbitrary initial data on the line and general interface conditions prescribed at the origin. It employs a novel implementation of Fokas' unified transform method for a fourth-order operator.

Significance. If the derivations hold, the explicit contour-integral formulas enable direct exploration of regularity, asymptotic behavior, and other qualitative properties, while also supporting well-posedness studies for nonlinear counterparts and free-boundary problems. The extension of the Fokas method to fourth-order operators with general single-point interface conditions represents a technical advance. The stress-test concern that the algebraic system for spectral functions may fail to close for arbitrary interface conditions does not land on reading the manuscript; the global relations are assembled and the resulting linear system is solved explicitly with the required invertibility verified in the relevant sectors.

minor comments (3)

Abstract: the phrasing 'spectacular variety of phenomena' is informal for a mathematics journal; a more neutral term such as 'wide range' would be preferable.
§2: the statement of the general interface conditions would be clearer if accompanied by an explicit enumeration or table listing the four conditions and their coefficients.
§4.1: a short remark on how the new representations reduce to the classical Fourier solution when the interface conditions are homogeneous would aid readability.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive and careful assessment of our manuscript. The referee's summary correctly identifies the core contribution: new explicit contour-integral representations for the fully non-homogeneous linear Cahn-Hilliard interface problem obtained via a novel application of the Fokas unified transform method to a fourth-order operator. We are gratified that the technical advance and its potential utility for regularity, asymptotics, and nonlinear extensions are recognized. We will incorporate minor revisions to further clarify the presentation.

Circularity Check

0 steps flagged

No circularity: derivation relies on independent Fokas-method closure for fourth-order interface problem.

full rationale

The paper presents explicit contour-integral representations obtained by applying the unified transform method to the linearized Cahn-Hilliard operator on the line with a single interface at x=0. The abstract and method description assert that global relations are written on each half-line, the resulting linear system for the unknown spectral functions is solved, and the contour integrals are then written down. No quoted equation or step reduces the claimed representations to a fitted parameter, a self-definition, or a prior self-citation that itself lacks independent verification. The central construction is therefore self-contained against external benchmarks (the classical Fokas framework and standard Fourier analysis on half-lines) and receives score 0.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The derivation rests on standard tools of complex analysis and Fourier methods; no free parameters, invented entities, or ad-hoc axioms are indicated in the abstract.

axioms (1)

standard math Standard properties of contour integration and the Fourier transform in the complex plane for fourth-order linear PDEs
Invoked to obtain the integral representations from the unified transform.

pith-pipeline@v0.9.0 · 5687 in / 1279 out tokens · 39622 ms · 2026-05-20T03:17:59.727952+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

A novel implementation of Fokas’ unified transform method is in force herein for a fourth-order operator for the first time... explicit formulae... contour integrals in the complex Fourier plane
IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

global relation... mappings ψ_R, φ_R... system of equations (2.6), (2.7), (3.7), (3.8) and (4.1)

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

39 extracted references · 39 canonical work pages

[1]

Cahn and J.E

J.W. Cahn and J.E. Hilliard, Free energy of a nonuniform system I. Interfacial free energy, J. Chem. Phys. 28, (1958)

work page 1958
[2]

Cahn, On spinodal decomposition, Acta Metall

J.W. Cahn, On spinodal decomposition, Acta Metall. 9, 795-801, (1961)

work page 1961
[3]

Novick-Cohen, The Cahn-Hilliard equation, in Handbook of Differential Equations, Evolutionary Partial Differential Equations, 4, (eds

A. Novick-Cohen, The Cahn-Hilliard equation, in Handbook of Differential Equations, Evolutionary Partial Differential Equations, 4, (eds. C. M. Dafermos and M. Pokorny), Elsevier, Amsterdam, 201–228, (2008)

work page 2008
[4]

Miranville, The Cahn-Hilliard Equation: Recent Advances and Applications, CBMS-NSF Regional Conference Series in Applied Mathematics 95, SIAM (2019)

A. Miranville, The Cahn-Hilliard Equation: Recent Advances and Applications, CBMS-NSF Regional Conference Series in Applied Mathematics 95, SIAM (2019). A. Chatziafratis, A. Miranville, T. Ozawa 17

work page 2019
[5]

Chatziafratis, A

A. Chatziafratis, A. Miranville, G. Karali, A.S. Fokas, E.C. Aifantis, Higher-order diffusion and Cahn–Hilliard- type models revisited on the half-line, Math. Models Methods Appl. Sci. (2025)

work page 2025
[6]

Aifantis, Internal length gradient (ILG) material mechanics across scales and disciplines, Adv

E.C. Aifantis, Internal length gradient (ILG) material mechanics across scales and disciplines, Adv. Appl. Mech. 49 (2016)

work page 2016
[7]

Aifantis, J.B

E.C. Aifantis, J.B. Serrin, The mechanical theory of fluid interfaces and Maxwell's rule, J. Colloid Interf. Sci. 96, 517-529 (1983)

work page 1983
[8]

N. D. Alikakos, G. Fusco, G. Karali, Motion of bubbles towards the boundary for the Cahn-Hilliard equation, Eur J Appl Math 15, 103-124, (2004)

work page 2004
[9]

Miranville, The Cahn-Hilliard equation with a nonlinear source term, J

A. Miranville, The Cahn-Hilliard equation with a nonlinear source term, J. Differential Equations 294, 88-117, (2021)

work page 2021
[10]

R., & Bazant, M

Ferguson, T. R., & Bazant, M. Z., Nonequilibrium thermodynamics of porous electrodes. Journal of The Electrochemical Society, 159(12), A1967-A1985, (2012)

work page 2012
[11]

Z., Phase separation dynamics in isotropic ion-intercalation particles

Zeng, Y., & Bazant, M. Z., Phase separation dynamics in isotropic ion-intercalation particles. SIAM Journal on Applied Mathematics, 74(4), 980-1004, (2014)

work page 2014
[12]

Discrete and Continuous Dynamical Systems-Series B, 19(7), 2013-2026, (2014)

Cherfils, L., Miranville, A., & Zelik, S., On a generalized Cahn-Hilliard equation with biological applications. Discrete and Continuous Dynamical Systems-Series B, 19(7), 2013-2026, (2014)

work page 2013
[13]

F., & Signori, A., On a phase field model of Cahn–Hilliard type for tumour growth with mechanical effects

Garcke, H., Lam, K. F., & Signori, A., On a phase field model of Cahn–Hilliard type for tumour growth with mechanical effects. Nonlinear Analysis: Real World Applications, 57, 103192, (2021)

work page 2021
[14]

J., & Topaz, C

Bernoff, A. J., & Topaz, C. M., Biological aggregation driven by social and environmental factors: A nonlocal model and its degenerate Cahn--Hilliard approximation. SIAM Journal on Applied Dynamical Systems, 15(3), 1528- 1562, (2016)

work page 2016
[15]

SIAM Journal on Mathematical Analysis, 52(4), 3843-3880, (2020)

Cucchi, A., Mellet, A., & Meunier, N., A Cahn--Hilliard Model for Cell Motility. SIAM Journal on Mathematical Analysis, 52(4), 3843-3880, (2020)

work page 2020
[16]

Fakih, H., Mghames, R., & Nasreddine, N., On the Cahn–Hilliard equation with mass source for biological applications. Commun. Pure Appl. Anal, 20(2), 495-510, (2021)

work page 2021
[17]

M., Generalized Cahn-Hilliard equation for biological applications

Khain, E., & Sander, L. M., Generalized Cahn-Hilliard equation for biological applications. Physical Review E—Statistical, Nonlinear, and Soft Matter Physics, 77(5), 051129, (2008)

work page 2008
[18]

W., Theory of thermal grooving

Mullins, W. W., Theory of thermal grooving. Journal of Applied Physics, 28(3), 333-339, (1957)

work page 1957
[19]

Fokas, A new transform method for evolution partial differential equations, IMA J

Athanassios S. Fokas, A new transform method for evolution partial differential equations, IMA J. Appl. Math. 67, 559-590 (2002); A Unified Approach to Boundary Value Problems, CBMS-NSF Series Appl. Math. 78, SIAM (2008)

work page 2002
[20]

S., & Pelloni, B

Fokas, A. S., & Pelloni, B. (Eds.). Unified Transform for Boundary Value Problems: Applications and Advances. Society for Industrial and Applied Mathematics, (2014)

work page 2014
[21]

A. S. Fokas, E. A. Spence, Synthesis, as opposed to separation, of variables, SIAM Review 54 (2012)

work page 2012
[22]

Deconinck, T

B. Deconinck, T. Trogdon, V. Vasan, The method of Fokas for solving linear partial differential equations, SIAM Review 56, 159-86 (2014)

work page 2014
[23]

Chatziafratis, A.S

A. Chatziafratis, A.S. Fokas, K. Kalimeris, The Fokas method for evolution partial differential equations, Partial Differ. Equ. Appl. Math. (2025)

work page 2025
[24]

E., Non-steady-state heat conduction in composite walls

Deconinck, B., Pelloni, B., Sheils, N. E., Non-steady-state heat conduction in composite walls. Proc R Soc A (2014)

work page 2014
[25]

E., Smith, D

Deconinck, B., Sheils, N. E., Smith, D. A., The linear KdV equation with an interface. Comm Math Phys (2016)

work page 2016
[26]

Luca, J.G

E. Luca, J.G. Marshall, A. Chatziafratis, Thermal contact resistance in two-phase media with arbitrarily shaped adiabatic fractures, preprint (2026)

work page 2026
[27]

Chatziafratis, T

A. Chatziafratis, T. Ozawa, Non-standard initial-boundary-value and interface problems for the linear BBM equation, Discrete Contin Dyn Syst-S (2026)

work page 2026
[28]

J.L. Bona, A. Chatziafratis, H. Chen, S. Kamvissis, The linearised BBM equation on the half-line revisited, Lett. Math. Phys. 114 (2024)

work page 2024
[29]

M. M. Cavalcanti, A. Chatziafratis, and L. Rosier. A unified approach to lack of controllability for linear evolution equations on quarter-planes. preprint (2025)

work page 2025
[30]

Chatziafratis, E.C

A. Chatziafratis, E.C. Aifantis, A. Carbery, A.S. Fokas, Integral representations for the double-diffusion system on the half-line, Z. Angew. Math. Phys. 75 (2024)

work page 2024
[31]

Chatziafratis, A.S

A. Chatziafratis, A.S. Fokas, E.C. Aifantis, On Barenblatt’s pseudoparabolic equation on the half-line via the Fokas method, Z. Angew. Math. Mech. (2024)

work page 2024
[32]

Chatziafratis, C

A. Chatziafratis, C. Giorgi, A. Miranville, F. Zullo, On generalized d’Alembert-type integral representations for the damped wave equation on the quarter-plane, preprint (2025)

work page 2025
[33]

Chatziafratis, L

A. Chatziafratis, L. Grafakos, S. Kamvissis, Long-range instabilities for linear evolution PDE on semi-bounded domains, Dyn. PDE 21 (2024). A. Chatziafratis, A. Miranville, T. Ozawa 18

work page 2024
[34]

Chatziafratis, S

A. Chatziafratis, S. Kamvissis, Infinity of solutions to initial-boundary value problems for linear constant- coefficient evolution PDEs on semi-infinite intervals, Bull. London Math. Soc. (2025)

work page 2025
[35]

Chatziafratis, S

A. Chatziafratis, S. Kamvissis, I. G. Stratis, Boundary behavior of the solution to the linear KdV equation on the half-line, Stud. Appl. Math. (2023)

work page 2023
[36]

Chatziafratis, G

A. Chatziafratis, G. Karali, C. E. Synolakis, Analytical solution for the linearized Whitham-Broer-Kaup system on the half-line, Stud. Appl. Math. (2026)

work page 2026
[37]

Chatziafratis, D

A. Chatziafratis, D. Mantzavinos, Boundary behavior for the heat equation on the half-line, Math. Meth. Appl. Sci. (2022)

work page 2022
[38]

Chatziafratis and T

A. Chatziafratis and T. Ozawa. New instability, blow-up and break-down effects for Sobolev-type evolution PDE: asymptotic analysis for a celebrated pseudo-parabolic model on the quarter-plane. Partial Differ. Equ. Appl. 5(30), (2024)

work page 2024
[39]

Chatziafratis, T

A. Chatziafratis, T. Ozawa, S.-F. Tian, Rigorous analysis of the unified transform method and long-range instabilities for the inhomogeneous time-dependent Schrödinger equation on the quarter-plane, Math. Annalen 389 (2023)

work page 2023

[1] [1]

Cahn and J.E

J.W. Cahn and J.E. Hilliard, Free energy of a nonuniform system I. Interfacial free energy, J. Chem. Phys. 28, (1958)

work page 1958

[2] [2]

Cahn, On spinodal decomposition, Acta Metall

J.W. Cahn, On spinodal decomposition, Acta Metall. 9, 795-801, (1961)

work page 1961

[3] [3]

Novick-Cohen, The Cahn-Hilliard equation, in Handbook of Differential Equations, Evolutionary Partial Differential Equations, 4, (eds

A. Novick-Cohen, The Cahn-Hilliard equation, in Handbook of Differential Equations, Evolutionary Partial Differential Equations, 4, (eds. C. M. Dafermos and M. Pokorny), Elsevier, Amsterdam, 201–228, (2008)

work page 2008

[4] [4]

Miranville, The Cahn-Hilliard Equation: Recent Advances and Applications, CBMS-NSF Regional Conference Series in Applied Mathematics 95, SIAM (2019)

A. Miranville, The Cahn-Hilliard Equation: Recent Advances and Applications, CBMS-NSF Regional Conference Series in Applied Mathematics 95, SIAM (2019). A. Chatziafratis, A. Miranville, T. Ozawa 17

work page 2019

[5] [5]

Chatziafratis, A

A. Chatziafratis, A. Miranville, G. Karali, A.S. Fokas, E.C. Aifantis, Higher-order diffusion and Cahn–Hilliard- type models revisited on the half-line, Math. Models Methods Appl. Sci. (2025)

work page 2025

[6] [6]

Aifantis, Internal length gradient (ILG) material mechanics across scales and disciplines, Adv

E.C. Aifantis, Internal length gradient (ILG) material mechanics across scales and disciplines, Adv. Appl. Mech. 49 (2016)

work page 2016

[7] [7]

Aifantis, J.B

E.C. Aifantis, J.B. Serrin, The mechanical theory of fluid interfaces and Maxwell's rule, J. Colloid Interf. Sci. 96, 517-529 (1983)

work page 1983

[8] [8]

N. D. Alikakos, G. Fusco, G. Karali, Motion of bubbles towards the boundary for the Cahn-Hilliard equation, Eur J Appl Math 15, 103-124, (2004)

work page 2004

[9] [9]

Miranville, The Cahn-Hilliard equation with a nonlinear source term, J

A. Miranville, The Cahn-Hilliard equation with a nonlinear source term, J. Differential Equations 294, 88-117, (2021)

work page 2021

[10] [10]

R., & Bazant, M

Ferguson, T. R., & Bazant, M. Z., Nonequilibrium thermodynamics of porous electrodes. Journal of The Electrochemical Society, 159(12), A1967-A1985, (2012)

work page 2012

[11] [11]

Z., Phase separation dynamics in isotropic ion-intercalation particles

Zeng, Y., & Bazant, M. Z., Phase separation dynamics in isotropic ion-intercalation particles. SIAM Journal on Applied Mathematics, 74(4), 980-1004, (2014)

work page 2014

[12] [12]

Discrete and Continuous Dynamical Systems-Series B, 19(7), 2013-2026, (2014)

Cherfils, L., Miranville, A., & Zelik, S., On a generalized Cahn-Hilliard equation with biological applications. Discrete and Continuous Dynamical Systems-Series B, 19(7), 2013-2026, (2014)

work page 2013

[13] [13]

F., & Signori, A., On a phase field model of Cahn–Hilliard type for tumour growth with mechanical effects

Garcke, H., Lam, K. F., & Signori, A., On a phase field model of Cahn–Hilliard type for tumour growth with mechanical effects. Nonlinear Analysis: Real World Applications, 57, 103192, (2021)

work page 2021

[14] [14]

J., & Topaz, C

Bernoff, A. J., & Topaz, C. M., Biological aggregation driven by social and environmental factors: A nonlocal model and its degenerate Cahn--Hilliard approximation. SIAM Journal on Applied Dynamical Systems, 15(3), 1528- 1562, (2016)

work page 2016

[15] [15]

SIAM Journal on Mathematical Analysis, 52(4), 3843-3880, (2020)

Cucchi, A., Mellet, A., & Meunier, N., A Cahn--Hilliard Model for Cell Motility. SIAM Journal on Mathematical Analysis, 52(4), 3843-3880, (2020)

work page 2020

[16] [16]

Fakih, H., Mghames, R., & Nasreddine, N., On the Cahn–Hilliard equation with mass source for biological applications. Commun. Pure Appl. Anal, 20(2), 495-510, (2021)

work page 2021

[17] [17]

M., Generalized Cahn-Hilliard equation for biological applications

Khain, E., & Sander, L. M., Generalized Cahn-Hilliard equation for biological applications. Physical Review E—Statistical, Nonlinear, and Soft Matter Physics, 77(5), 051129, (2008)

work page 2008

[18] [18]

W., Theory of thermal grooving

Mullins, W. W., Theory of thermal grooving. Journal of Applied Physics, 28(3), 333-339, (1957)

work page 1957

[19] [19]

Fokas, A new transform method for evolution partial differential equations, IMA J

Athanassios S. Fokas, A new transform method for evolution partial differential equations, IMA J. Appl. Math. 67, 559-590 (2002); A Unified Approach to Boundary Value Problems, CBMS-NSF Series Appl. Math. 78, SIAM (2008)

work page 2002

[20] [20]

S., & Pelloni, B

Fokas, A. S., & Pelloni, B. (Eds.). Unified Transform for Boundary Value Problems: Applications and Advances. Society for Industrial and Applied Mathematics, (2014)

work page 2014

[21] [21]

A. S. Fokas, E. A. Spence, Synthesis, as opposed to separation, of variables, SIAM Review 54 (2012)

work page 2012

[22] [22]

Deconinck, T

B. Deconinck, T. Trogdon, V. Vasan, The method of Fokas for solving linear partial differential equations, SIAM Review 56, 159-86 (2014)

work page 2014

[23] [23]

Chatziafratis, A.S

A. Chatziafratis, A.S. Fokas, K. Kalimeris, The Fokas method for evolution partial differential equations, Partial Differ. Equ. Appl. Math. (2025)

work page 2025

[24] [24]

E., Non-steady-state heat conduction in composite walls

Deconinck, B., Pelloni, B., Sheils, N. E., Non-steady-state heat conduction in composite walls. Proc R Soc A (2014)

work page 2014

[25] [25]

E., Smith, D

Deconinck, B., Sheils, N. E., Smith, D. A., The linear KdV equation with an interface. Comm Math Phys (2016)

work page 2016

[26] [26]

Luca, J.G

E. Luca, J.G. Marshall, A. Chatziafratis, Thermal contact resistance in two-phase media with arbitrarily shaped adiabatic fractures, preprint (2026)

work page 2026

[27] [27]

Chatziafratis, T

A. Chatziafratis, T. Ozawa, Non-standard initial-boundary-value and interface problems for the linear BBM equation, Discrete Contin Dyn Syst-S (2026)

work page 2026

[28] [28]

J.L. Bona, A. Chatziafratis, H. Chen, S. Kamvissis, The linearised BBM equation on the half-line revisited, Lett. Math. Phys. 114 (2024)

work page 2024

[29] [29]

M. M. Cavalcanti, A. Chatziafratis, and L. Rosier. A unified approach to lack of controllability for linear evolution equations on quarter-planes. preprint (2025)

work page 2025

[30] [30]

Chatziafratis, E.C

A. Chatziafratis, E.C. Aifantis, A. Carbery, A.S. Fokas, Integral representations for the double-diffusion system on the half-line, Z. Angew. Math. Phys. 75 (2024)

work page 2024

[31] [31]

Chatziafratis, A.S

A. Chatziafratis, A.S. Fokas, E.C. Aifantis, On Barenblatt’s pseudoparabolic equation on the half-line via the Fokas method, Z. Angew. Math. Mech. (2024)

work page 2024

[32] [32]

Chatziafratis, C

A. Chatziafratis, C. Giorgi, A. Miranville, F. Zullo, On generalized d’Alembert-type integral representations for the damped wave equation on the quarter-plane, preprint (2025)

work page 2025

[33] [33]

Chatziafratis, L

A. Chatziafratis, L. Grafakos, S. Kamvissis, Long-range instabilities for linear evolution PDE on semi-bounded domains, Dyn. PDE 21 (2024). A. Chatziafratis, A. Miranville, T. Ozawa 18

work page 2024

[34] [34]

Chatziafratis, S

A. Chatziafratis, S. Kamvissis, Infinity of solutions to initial-boundary value problems for linear constant- coefficient evolution PDEs on semi-infinite intervals, Bull. London Math. Soc. (2025)

work page 2025

[35] [35]

Chatziafratis, S

A. Chatziafratis, S. Kamvissis, I. G. Stratis, Boundary behavior of the solution to the linear KdV equation on the half-line, Stud. Appl. Math. (2023)

work page 2023

[36] [36]

Chatziafratis, G

A. Chatziafratis, G. Karali, C. E. Synolakis, Analytical solution for the linearized Whitham-Broer-Kaup system on the half-line, Stud. Appl. Math. (2026)

work page 2026

[37] [37]

Chatziafratis, D

A. Chatziafratis, D. Mantzavinos, Boundary behavior for the heat equation on the half-line, Math. Meth. Appl. Sci. (2022)

work page 2022

[38] [38]

Chatziafratis and T

A. Chatziafratis and T. Ozawa. New instability, blow-up and break-down effects for Sobolev-type evolution PDE: asymptotic analysis for a celebrated pseudo-parabolic model on the quarter-plane. Partial Differ. Equ. Appl. 5(30), (2024)

work page 2024

[39] [39]

Chatziafratis, T

A. Chatziafratis, T. Ozawa, S.-F. Tian, Rigorous analysis of the unified transform method and long-range instabilities for the inhomogeneous time-dependent Schrödinger equation on the quarter-plane, Math. Annalen 389 (2023)

work page 2023