The generalized porous medium equation on graphs: existence and uniqueness of solutions with ℓ1 data

We study solutions of the generalized porous medium equation on infinite graphs. For nonnegative or nonpositive integrable data, we prove the existence and uniqueness of mild solutions on any graph. For changing sign integrable data, we show existence and uniqueness under extra assumptions such as l...

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Bibliographic Details
Published inCalculus of variations and partial differential equations Vol. 61; no. 5
Main Authors Bianchi, Davide, Setti, Alberto G., Wojciechowski, Radosław K.
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 2022
Springer Nature B.V
Subjects
Analysis
Calculus of Variations and Optimal Control; Optimization
Control
Graphs
Lower bounds
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Porous media
Systems Theory
Theoretical
Uniqueness
05C22
35A02
05C63
35A01
76S05
47H06
35K55
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Summary:We study solutions of the generalized porous medium equation on infinite graphs. For nonnegative or nonpositive integrable data, we prove the existence and uniqueness of mild solutions on any graph. For changing sign integrable data, we show existence and uniqueness under extra assumptions such as local finiteness or a uniform lower bound on the node measure.
ISSN:0944-2669
1432-0835
DOI:10.1007/s00526-022-02249-w