Paper Citation Record · LEDGER

The generalized porous medium equation on graphs: well-posedness, extinction, and mass conservation

As of 21 August 2026, this Paper Citation Record lists 65 of 65 outbound references and 1 inbound Pith citation observation for arXiv:2607.23091.

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2607.23091 v1

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measured 65 of 65 reference resolution

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Source: pith, observed 2026-08-16T00:39:28.670081Z

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65 of 65 outbound references displayed

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Outbound references

Observation f50fb880-83cd-42f3-8d83-0851bfe99d34 · outbound

This paper cites Rates of convergence to non-degenerate asymptotic profiles for fast diffusion via energy methods.

The generalized porous medium equation on graphs: well-posedness, extinction, and mass conservation Rates of convergence to non-degenerate asymptotic profiles for fast diffusion via energy methods

Reference 1

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Observation ab918e06-f3f8-4917-82af-f506e103a24b · outbound

This paper cites The porous medium equation.

The generalized porous medium equation on graphs: well-posedness, extinction, and mass conservation The porous medium equation

Reference 2

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Observation 56f6a81a-5de6-46ea-8276-48f4c02727b6 · outbound

This paper cites A comparison principle for the porous medium equation and its consequences.

The generalized porous medium equation on graphs: well-posedness, extinction, and mass conservation A comparison principle for the porous medium equation and its consequences

Reference 3

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This paper cites Barbu.Nonlinear differential equations of monotone types in Banach spaces.

The generalized porous medium equation on graphs: well-posedness, extinction, and mass conservation Barbu.Nonlinear differential equations of monotone types in Banach spaces

Reference 4

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This paper cites The Degree of Polynomial Growth of Finitely Generated Nilpotent Groups.

The generalized porous medium equation on graphs: well-posedness, extinction, and mass conservation The Degree of Polynomial Growth of Finitely Generated Nilpotent Groups

Reference 5

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This paper cites Nonlinear evolution equations in Banach spaces.

The generalized porous medium equation on graphs: well-posedness, extinction, and mass conservation Nonlinear evolution equations in Banach spaces

Reference 6

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Observation b37aae74-da79-4bd2-b0e7-8a46b74517a5 · outbound

This paper cites Semilinear diffusion equations on infinite graphs: the dissipative and Lipschitz cases.

The generalized porous medium equation on graphs: well-posedness, extinction, and mass conservation Semilinear diffusion equations on infinite graphs: the dissipative and Lipschitz cases

Reference 7

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Observation 9c30e007-0ac1-4ec9-bed1-3937e6df780e · outbound

This paper cites The fractional Porous Medium Equation on graphs.

The generalized porous medium equation on graphs: well-posedness, extinction, and mass conservation The fractional Porous Medium Equation on graphs

Reference 8

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Observation 69de002a-b7ed-43b1-af5c-9abe6140022e · outbound

This paper cites Phragm\`en-Lindel\"of type theorems for parabolic equations on infinite graphs.

The generalized porous medium equation on graphs: well-posedness, extinction, and mass conservation Phragm\`en-Lindel\"of type theorems for parabolic equations on infinite graphs

Reference 9

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Observation 27352d9e-57f6-40c8-ac7e-a2177a5eb306 · outbound

This paper cites On the accretivity and m-accretivity of Laplacians and porous medium-type operators on graphs.

The generalized porous medium equation on graphs: well-posedness, extinction, and mass conservation On the accretivity and m-accretivity of Laplacians and porous medium-type operators on graphs

Reference 10

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Observation d087a90a-2ba0-48de-b9ce-30e72254cb97 · outbound

This paper cites Laplacian cut-offs, porous and fast diffusion on manifolds and other applications.

The generalized porous medium equation on graphs: well-posedness, extinction, and mass conservation Laplacian cut-offs, porous and fast diffusion on manifolds and other applications

Reference 11

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Observation 03439ab3-4c54-4b70-a9f5-699616bff7bc · outbound

This paper cites The generalized porous medium equation on graphs: exis- tence and uniqueness of solutions withℓ 1 data.

The generalized porous medium equation on graphs: well-posedness, extinction, and mass conservation The generalized porous medium equation on graphs: exis- tence and uniqueness of solutions withℓ 1 data

Reference 12

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Observation 3eafe7d9-e5ce-4d03-9dc7-0c7d121b017c · outbound

This paper cites The Cauchy-Dirichlet problem for the fast diffusion equation on bounded do- mains.

The generalized porous medium equation on graphs: well-posedness, extinction, and mass conservation The Cauchy-Dirichlet problem for the fast diffusion equation on bounded do- mains

Reference 13

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Observation 2575ca80-9819-4886-b1a2-b05c2988cc2f · outbound

This paper cites Positivity, local smoothing, and Harnack inequalities for very fast diffusion equations.

The generalized porous medium equation on graphs: well-posedness, extinction, and mass conservation Positivity, local smoothing, and Harnack inequalities for very fast diffusion equations

Reference 14

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This paper cites Cauchy-Dirichlet problems for the porous medium equation.

The generalized porous medium equation on graphs: well-posedness, extinction, and mass conservation Cauchy-Dirichlet problems for the porous medium equation

Reference 15

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Observation 87def246-7292-4e00-8ae2-d77fe54fb0c8 · outbound

This paper cites Aronson–B ´enilan estimates for the fast diffusion equation under the Ricci flow.

The generalized porous medium equation on graphs: well-posedness, extinction, and mass conservation Aronson–B ´enilan estimates for the fast diffusion equation under the Ricci flow

Reference 16

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Observation aa63d47e-66ef-410d-8294-f729852aa169 · outbound

This paper cites Asymptotics near extinction for nonlinear fast diffusion on a bounded domain.

The generalized porous medium equation on graphs: well-posedness, extinction, and mass conservation Asymptotics near extinction for nonlinear fast diffusion on a bounded domain

Reference 17

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Observation 07c63e83-675c-4666-9ad7-410f1fc5879b · outbound

This paper cites Near field asymptotic behavior for the porous medium equation on the half-line.

The generalized porous medium equation on graphs: well-posedness, extinction, and mass conservation Near field asymptotic behavior for the porous medium equation on the half-line

Reference 18

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Observation 77315515-e035-41ac-ac4f-e77c6243d76a · outbound

This paper cites Near-field asymptotics for the porous medium equation in exterior do- mains. The critical two-dimensional case.

The generalized porous medium equation on graphs: well-posedness, extinction, and mass conservation Near-field asymptotics for the porous medium equation in exterior do- mains. The critical two-dimensional case

Reference 19

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Observation 25095a17-9adb-456f-975f-2d0c2cded204 · outbound

This paper cites Generation of semi-groups of nonlinear transformations on general Banach spaces.

The generalized porous medium equation on graphs: well-posedness, extinction, and mass conservation Generation of semi-groups of nonlinear transformations on general Banach spaces

Reference 20

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This paper cites Maximum principle for parabolic inequalities and the heat flow on open manifolds.

The generalized porous medium equation on graphs: well-posedness, extinction, and mass conservation Maximum principle for parabolic inequalities and the heat flow on open manifolds

Reference 21

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This paper cites Aronson–B ´enilan gradient estimates for porous medium equations under lower bounds ofN- weighted Ricci curvature withN <0.

The generalized porous medium equation on graphs: well-posedness, extinction, and mass conservation Aronson–B ´enilan gradient estimates for porous medium equations under lower bounds ofN- weighted Ricci curvature withN <0

Reference 22

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This paper cites Parabolicity and stochastic completeness of manifolds in terms of the Green formula.

The generalized porous medium equation on graphs: well-posedness, extinction, and mass conservation Parabolicity and stochastic completeness of manifolds in terms of the Green formula

Reference 23

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The generalized porous medium equation on graphs: well-posedness, extinction, and mass conservation The porous medium equation on noncompact manifolds with non- negative Ricci curvature: A Green function approach

Reference 24

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This paper cites Smoothing effects for the porous medium equation on Cartan–Hadamard mani- folds.

The generalized porous medium equation on graphs: well-posedness, extinction, and mass conservation Smoothing effects for the porous medium equation on Cartan–Hadamard mani- folds

Reference 25

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This paper cites A porous medium equation with rough weights: sharp Widder theory.

The generalized porous medium equation on graphs: well-posedness, extinction, and mass conservation A porous medium equation with rough weights: sharp Widder theory

Reference 26

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The generalized porous medium equation on graphs: well-posedness, extinction, and mass conservation The porous medium equation with large initial data on negatively curved Riemannian manifolds

Reference 27

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The generalized porous medium equation on graphs: well-posedness, extinction, and mass conservation The porous medium equation with measure data on negatively curved Riemannian manifolds

Reference 28

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The generalized porous medium equation on graphs: well-posedness, extinction, and mass conservation The porous medium equation on Riemannian manifolds with negative curvature. The large-time behaviour

Reference 29

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The generalized porous medium equation on graphs: well-posedness, extinction, and mass conservation The porous medium equation on Riemannian manifolds with negative curvature: the superquadratic case

Reference 30

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The generalized porous medium equation on graphs: well-posedness, extinction, and mass conservation Croissance polynomiale et p ´eriodes des fonctions harmoniques

Reference 31

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The generalized porous medium equation on graphs: well-posedness, extinction, and mass conservation Global properties of Dirichlet forms in terms of Green’s formula

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The generalized porous medium equation on graphs: well-posedness, extinction, and mass conservation Cheeger estimates of Dirichlet-to-Neumann operators on infinite subgraphs of graphs

Reference 33

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The generalized porous medium equation on graphs: well-posedness, extinction, and mass conservation The existence of extremal functions for discrete Sobolev inequalities on lattice graphs

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The generalized porous medium equation on graphs: well-posedness, extinction, and mass conservation Stochastic completeness for graphs with curvature dimension conditions

Reference 35

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The generalized porous medium equation on graphs: well-posedness, extinction, and mass conservation Time regularity and long-time behavior of parabolicp-Laplace equations on infinite graphs

Reference 36

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The generalized porous medium equation on graphs: well-posedness, extinction, and mass conservation Bubbling and extinction for some fast diffusion equations in bounded domains

Reference 37

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The generalized porous medium equation on graphs: well-posedness, extinction, and mass conservation Extinction profiles for the Sobolev critical fast diffusion equation in bounded domains. I. One bubble dynamics

Reference 38

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The generalized porous medium equation on graphs: well-posedness, extinction, and mass conservation Optimal boundary regularity for fast diffusion equations in bounded domains

Reference 39

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The generalized porous medium equation on graphs: well-posedness, extinction, and mass conservation Regularity of solutions to the Dirichlet problem for fast diffusion equations

Reference 40

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Observation b13708cf-46c4-405d-823e-7f534d5a734f · outbound

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The generalized porous medium equation on graphs: well-posedness, extinction, and mass conservation Singular extinction profiles of solutions to some fast diffusion equations

Reference 41

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Observation a2b62bc7-ae86-4139-9a43-c46c4c2b8976 · outbound

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The generalized porous medium equation on graphs: well-posedness, extinction, and mass conservation Dirichlet forms and stochastic completeness of graphs and subgraphs

Reference 42

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Observation b713f8bc-2f50-43a3-9707-ae97b99c027e · outbound

This paper cites Unbounded Laplacians on graphs: basic spectral properties and the heat equation.

The generalized porous medium equation on graphs: well-posedness, extinction, and mass conservation Unbounded Laplacians on graphs: basic spectral properties and the heat equation

Reference 43

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The generalized porous medium equation on graphs: well-posedness, extinction, and mass conservation Keller, D

Reference 44

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The generalized porous medium equation on graphs: well-posedness, extinction, and mass conservation Gaussian upper bounds, volume doubling and Sobolev inequalities on graphs

Reference 45

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Observation 53b556b2-14b2-4c06-90e4-00ac335eee81 · outbound

This paper cites Flat fronts and stability for the porous medium equation.

The generalized porous medium equation on graphs: well-posedness, extinction, and mass conservation Flat fronts and stability for the porous medium equation

Reference 46

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The generalized porous medium equation on graphs: well-posedness, extinction, and mass conservation Perron’s method for the porous medium equation

Reference 47

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Observation 171b5b0a-e59a-46f5-a825-151b0c4de40e · outbound

This paper cites Porous medium equations with reactions on a metric graph.

The generalized porous medium equation on graphs: well-posedness, extinction, and mass conservation Porous medium equations with reactions on a metric graph

Reference 48

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Observation a77821d2-9d39-40c3-b0f3-c3510c143f17 · outbound

This paper cites Lakshmikantham and S.

The generalized porous medium equation on graphs: well-posedness, extinction, and mass conservation Lakshmikantham and S

Reference 49

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Observation 86f6fa89-f083-46f4-b469-6ef072e89bf9 · outbound

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The generalized porous medium equation on graphs: well-posedness, extinction, and mass conservation Gradient flows of generalized relative entropy and functional inequalities on graphs

Reference 50

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Observation 6a97c6ec-9702-419e-8501-c633ac7a5b95 · outbound

This paper cites Porous media equation on locally finite graphs.

The generalized porous medium equation on graphs: well-posedness, extinction, and mass conservation Porous media equation on locally finite graphs

Reference 51

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This paper cites A generalized conservation property for the heat semigroup on weighted man- ifolds.

The generalized porous medium equation on graphs: well-posedness, extinction, and mass conservation A generalized conservation property for the heat semigroup on weighted man- ifolds

Reference 52

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The generalized porous medium equation on graphs: well-posedness, extinction, and mass conservation Ollivier Ricci curvature for general graph Laplacians: heat equation, Laplacian comparison, non-explosion and diameter bounds

Reference 53

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The generalized porous medium equation on graphs: well-posedness, extinction, and mass conservation Nonlinear Integral Inequalities I

Reference 54

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This paper cites Gradient estimates for porous medium equations under the Ricci flow.

The generalized porous medium equation on graphs: well-posedness, extinction, and mass conservation Gradient estimates for porous medium equations under the Ricci flow

Reference 55

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Reference 56

Resolution: verified exact; doi, observed 2026-08-01T03:53:37.614296Z

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The generalized porous medium equation on graphs: well-posedness, extinction, and mass conservation Unresolved cited work

Reference 57

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The generalized porous medium equation on graphs: well-posedness, extinction, and mass conservation Unresolved cited work

Reference 58

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The generalized porous medium equation on graphs: well-posedness, extinction, and mass conservation Unresolved cited work

Reference 59

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This paper cites Eigenvalue estimates for the fractional Laplacian on lattice subgraphs.

The generalized porous medium equation on graphs: well-posedness, extinction, and mass conservation Eigenvalue estimates for the fractional Laplacian on lattice subgraphs

Reference 60

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This paper cites Some gradient estimates and Liouville properties of the fast diffusion equation on Riemannian manifolds.

The generalized porous medium equation on graphs: well-posedness, extinction, and mass conservation Some gradient estimates and Liouville properties of the fast diffusion equation on Riemannian manifolds

Reference 61

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This paper cites Woess.Random walks on infinite graphs and groups.

The generalized porous medium equation on graphs: well-posedness, extinction, and mass conservation Woess.Random walks on infinite graphs and groups

Reference 62

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The generalized porous medium equation on graphs: well-posedness, extinction, and mass conservation Heat kernel and essential spectrum of infinite graphs

Reference 63

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The generalized porous medium equation on graphs: well-posedness, extinction, and mass conservation Stochastic Completeness of Graphs

Reference 64

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The generalized porous medium equation on graphs: well-posedness, extinction, and mass conservation Fractional Laplace operator and related Schr¨odinger equations on locally finite graphs

Reference 65

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Pith citing papers

Observation e8d739d5-7adb-4ca1-8a24-5b90218f6997 · inbound

Nonlinear parabolic characterizations of stochastic completeness at infinity on weighted graphs cites this paper.

Nonlinear parabolic characterizations of stochastic completeness at infinity on weighted graphs The generalized porous medium equation on graphs: well-posedness, extinction, and mass conservation

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