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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Published in | Calculus of variations and partial differential equations Vol. 61; no. 5 |
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Main Authors | , , |
Format | Journal Article |
Language | English |
Published |
Berlin/Heidelberg
Springer Berlin Heidelberg
2022
Springer Nature B.V |
Subjects | |
Online Access | Get full text |
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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. |
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ISSN: | 0944-2669 1432-0835 |
DOI: | 10.1007/s00526-022-02249-w |