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Paper Citation Record · LEDGER

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

As of 8 August 2026, this Paper Citation Record lists 65 of 65 outbound references and 0 inbound Pith citation observations for arXiv:2607.23091.

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pith.paper-citation-record.v1
2607.23091 v1

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measured 65 of 65 reference resolution

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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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This paper cites The porous medium equation.

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

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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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

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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

Reference 32

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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

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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

Reference 34

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Observation bd8bf778-8c5e-490f-bc7e-1ce9a061cd08 · outbound

This paper cites Stochastic completeness for graphs with curvature dimension conditions.

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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source=pdf_text observed=2026-08-01T03:49:51.218040Z digest=sha256:bc6680d0631414a58c21ecb19b4c7c8b20b3ec27cf7e5c6490e301b332d4188f

Observation 8aeec2bb-fa06-40e9-b1e7-4f9f48583d5f · outbound

This paper cites Time regularity and long-time behavior of parabolicp-Laplace equations on infinite graphs.

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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source=pdf_text observed=2026-08-01T03:49:51.220844Z digest=sha256:8393f2369527f9bb7bec4ece78b37214cdda83bdeb6f2be0ad91296170c75cef

Observation 2a05fe0a-d8ea-46f3-970a-2e873ce84b33 · outbound

This paper cites Bubbling and extinction for some fast diffusion equations in bounded domains.

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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source=pdf_text observed=2026-08-01T03:49:51.223433Z digest=sha256:62c38e011c13f470cc1070d6f615b1d5715185eee7e06683b78905ad96ef1e26

Observation b4aaf4b8-1f8e-4b12-af8a-caaad2e287f1 · outbound

This paper cites Extinction profiles for the Sobolev critical fast diffusion equation in bounded domains. I. One bubble dynamics.

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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source=pdf_text observed=2026-08-01T03:49:51.225905Z digest=sha256:3716235b1d325ab9b822d7aefaf1a677722e0139db8e49e05a34f85d437a5088

Observation b3741300-7422-47fc-a883-13f3de7bf9d1 · outbound

This paper cites Optimal boundary regularity for fast diffusion equations in bounded domains.

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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source=pdf_text observed=2026-08-01T03:49:51.228397Z digest=sha256:e51a58771beaf6680d6317efe1c9f48fccd6953b90c0ef98fe1b84dbcc866ddf

Observation 9317dca3-98bf-4a1b-b75f-0cd68e421cd4 · outbound

This paper cites Regularity of solutions to the Dirichlet problem for fast diffusion equations.

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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source=pdf_text observed=2026-08-01T03:49:51.230964Z digest=sha256:5bb6e94cfbb8d28214b2d72db847d2afd3705bd9c234bab1c2f23473490bf6b5

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

This paper cites Singular extinction profiles of solutions to some fast diffusion equations.

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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source=pdf_text observed=2026-08-01T03:49:51.233450Z digest=sha256:d4830f6e094c194d0f9b8f889efa4a4e73300d2c1297f71e950569e3a26e9580

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

This paper cites Dirichlet forms and stochastic completeness of graphs and subgraphs.

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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source=pdf_text observed=2026-08-01T03:49:51.236171Z digest=sha256:07645ee114dd8c62b90da3e29518b5b10528de7f67b3da950b0605f25d3c6146

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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source=pdf_text observed=2026-08-01T03:49:51.238746Z digest=sha256:2985385d343d66359612bc4d85bd678d3e0170648afb0b1b5570e682b2b0380c

Observation 2d0583ba-5ccc-4598-934b-73c65bdeef12 · outbound

This paper cites Keller, D.

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

Reference 44

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source=pdf_text observed=2026-08-01T03:49:51.241377Z digest=sha256:391f3884dd48018d7edec5776d0c06022985d81781af392bd3358779798dad51

Observation f09702cc-03ee-4283-87ff-2e6078edcf34 · outbound

This paper cites Gaussian upper bounds, volume doubling and Sobolev inequalities on graphs.

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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source=pdf_text observed=2026-08-01T03:49:51.244419Z digest=sha256:676e6ca3636f78044158f643f9d98b55d3474b3696d9b40b9ff91de3a2c3f967

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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source=pdf_text observed=2026-08-01T03:49:51.247060Z digest=sha256:e876e64e1c986ce68b3dfd89792554b3e96077a06c243adf5ad99c6b6605a664

Observation 76085a8d-f5c2-4597-a353-745ff60dee56 · outbound

This paper cites Perron’s method for the porous medium equation.

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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verified exact
doi, observed 2026-08-01T03:53:38.061223Z

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source=pdf_text observed=2026-08-01T03:49:51.249534Z digest=sha256:a76804ff09e2902c51b9418fdf6e5c2d147c534388102af72bb42a901f0886dd

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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source=pdf_text observed=2026-08-01T03:49:51.252137Z digest=sha256:962380234c589e3a962fb159e4788b8ec7ee7a5394427c76845d0faa2a6a553b

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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source=pdf_text observed=2026-08-01T03:49:51.255206Z digest=sha256:868905d0483e108fab0f0f3820365c7225e4adf48cf1f8d5ba776ee684cf24fc

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

This paper cites Gradient flows of generalized relative entropy and functional inequalities on graphs.

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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source=pdf_text observed=2026-08-01T03:49:51.257777Z digest=sha256:9eb2b0907156528ef2dcc48e1d9a032a1afd9a95f045d5e9e7a127ae26a0d83a

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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source=pdf_text observed=2026-08-01T03:49:51.260438Z digest=sha256:c6d939fccadc68a13ec3fa4920777e543a6eb1a09708d5bfcff1c77f0314cd6c

Observation e7c4edcc-b646-4368-8ad7-9258842d2ab1 · outbound

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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source=pdf_text observed=2026-08-01T03:49:51.263334Z digest=sha256:4376b53fda09fdaae606873c88cf15fbeaeb31770ecc4d2b415129f4ec8b5c03

Observation 1f175ab1-cd62-4101-a8d3-387adde31d01 · outbound

This paper cites Ollivier Ricci curvature for general graph Laplacians: heat equation, Laplacian comparison, non-explosion and diameter bounds.

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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source=pdf_text observed=2026-08-01T03:49:51.265893Z digest=sha256:5c6b83e66e1f09780280b657cbee061abeaf8dd5f066a51b2f8005a91100bd65

Observation aed14a1c-ece0-4039-8876-22be221c3bc8 · outbound

This paper cites Nonlinear Integral Inequalities I.

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

Reference 54

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doi_truncated, observed 2026-08-01T03:53:37.758512Z

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source=pdf_text observed=2026-08-01T03:49:51.268512Z digest=sha256:1bae136259d64331ccccdfdbce1481c70b7821445d67002a3e5d3779593ff865

Observation 3b086bbf-533b-4138-8a35-c5a338b0234a · outbound

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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source=pdf_text observed=2026-08-01T03:49:51.271146Z digest=sha256:028652c0de8624844ef438aa24810866de9befc323c8160309086eb50f9e38bb

Observation e6269f77-f5f9-4325-9fa4-dbd0c6d6707c · outbound

This paper cites an unresolved cited work.

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

Reference 56

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No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-01T03:49:51.273667Z digest=sha256:56250c904d9cf1d89476c49d161f726a3306fc7f15b896a9a160efff5c60a379

Observation 6148876a-8d33-44b0-9703-0d16d4ad2378 · outbound

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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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source=pdf_text observed=2026-08-01T03:49:51.276512Z digest=sha256:94642a0996ab8baf46d8d888a91638a3bc1bd4dfed27926b247d231f1b1bcf13

Observation 142e0894-9c27-4ea3-97ef-c9a6923b217a · outbound

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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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source=pdf_text observed=2026-08-01T03:49:51.279264Z digest=sha256:737d0afb3d6d6df7835f5d7b1282c48dd1be3d2f69ba0e0f168cc6f7a8bdabde

Observation 6020eacf-f745-4e87-8a9b-fb87212a4a77 · outbound

This paper cites an unresolved cited work.

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

Reference 59

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source=pdf_text observed=2026-08-01T03:49:51.281802Z digest=sha256:96194c755a6c071ecd73792062bc8715e0ca9430afae5b6cd963bc7aaa4bd3ca

Observation 223ef9a3-c278-4700-83a9-2b4684852575 · outbound

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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source=pdf_text observed=2026-08-01T03:49:51.284584Z digest=sha256:a1a63aef31ade1b49e7ad8cd99274631c961062347961401a5d6fdcf29ce0893

Observation 930e41b2-d9a8-48bc-9a22-8e6a2e00d577 · outbound

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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source=pdf_text observed=2026-08-01T03:49:51.287398Z digest=sha256:eb76d8ed9dc5003b145639b51987709824a0547259550f0d4dd0a225167f4076

Observation 77f26677-0623-412e-a4c2-69d2b3ccf3d9 · outbound

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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source=pdf_text observed=2026-08-01T03:49:51.290070Z digest=sha256:77e175ad1f0bc9581d10e4826a40ce3c15c6394b3c87680a57b4c4025cd4bd0e

Observation 68bbe289-aedd-4bef-a476-a164b982c890 · outbound

This paper cites Heat kernel and essential spectrum of infinite graphs.

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

Reference 63

Resolution
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source=pdf_text observed=2026-08-01T03:49:51.292804Z digest=sha256:8086f001b0f160509a9dd855ea83ed9e907637e154c9bf54e696dbefc1db77f6

Observation 333ef06e-ae8d-4810-86d7-a919db53900f · outbound

This paper cites Stochastic Completeness of Graphs.

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

Reference 64

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source=pdf_text observed=2026-08-01T03:49:51.295400Z digest=sha256:28ab79cc5edc22b6d9a58cb396c22cb3cf3b92bb8299f63e76d0e553bc0d7af8

Observation 74f6e501-3432-4477-8789-9b8a02fb6d6c · outbound

This paper cites Fractional Laplace operator and related Schr¨odinger equations on locally finite graphs.

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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source=pdf_text observed=2026-08-01T03:49:51.298244Z digest=sha256:82386c5170662a0ad1921f1baeb2405ff41e445f19d0e753e40e4233f63b9ace

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