Degenerate hyperbolic equations are approximated by uniformly hyperbolic ones to prove controllability in higher dimensions for the first time.
Title resolution pending
5 Pith papers cite this work. Polarity classification is still indexing.
5
Pith papers citing it
years
2026 5verdicts
UNVERDICTED 5representative citing papers
Null controllability is established for a multi-dimensional degenerate parabolic PDE with an interior degenerate point outside the control domain by approximating the system with uniformly elliptic equations and using Carleman estimates to obtain observability.
Courant's nodal domain theorem and the residual nature of simple eigenvalues under perturbations both hold for the degenerate elliptic operator A = -div(w ∇·) with w > 0 inside Ω and w = 0 on part of ∂Ω.
A quantitative weak unique continuation theorem is established for backward degenerate parabolic equations on annular domains with degenerate interior points by approximating with non-degenerate equations and applying Carleman estimates.
Shape design approximation proposed for degenerate PDEs, used to obtain Carleman estimates for null controllability of degenerate parabolic equations by avoiding second derivatives.
citing papers explorer
-
Approximation of Degenerate Hyperbolic Equations with Interior Degeneracy and Applications to Controllability
Degenerate hyperbolic equations are approximated by uniformly hyperbolic ones to prove controllability in higher dimensions for the first time.
-
Null Controllability for a Multi-Dimensional Degenerate Parabolic Equation with Degenerated Interior Point
Null controllability is established for a multi-dimensional degenerate parabolic PDE with an interior degenerate point outside the control domain by approximating the system with uniformly elliptic equations and using Carleman estimates to obtain observability.
-
Some Key Properties of Eigenfunctions Linked to Degenerate Elliptic Differential Operators
Courant's nodal domain theorem and the residual nature of simple eigenvalues under perturbations both hold for the degenerate elliptic operator A = -div(w ∇·) with w > 0 inside Ω and w = 0 on part of ∂Ω.
-
Quantitative Weak Unique Continuation on Annular Domains for Backward Degenerate Parabolic Equations with Degenerate Interior Points
A quantitative weak unique continuation theorem is established for backward degenerate parabolic equations on annular domains with degenerate interior points by approximating with non-degenerate equations and applying Carleman estimates.
-
A Shape Design Approximation for Degenerate Partial Differential Equations and Its Application
Shape design approximation proposed for degenerate PDEs, used to obtain Carleman estimates for null controllability of degenerate parabolic equations by avoiding second derivatives.