| Title:
|
Porous media equation on locally finite graphs (English) |
| Author:
|
Ma, Li |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
58 |
| Issue:
|
3 |
| Year:
|
2022 |
| Pages:
|
177-187 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper, we consider two typical problems on a locally finite connected graph. The first one is to study the Bochner formula for the Laplacian operator on a locally finite connected graph. The other one is to obtain global nontrivial nonnegative solution to porous-media equation via the use of Aronson-Benilan argument. We use the curvature dimension condition to give a characterization two point graph. We also give a porous-media equation criterion about stochastic completeness of the graph. There is not much work in the direction of the study of nonlinear heat equations on locally finite connected graphs. (English) |
| Keyword:
|
Bochner formula |
| Keyword:
|
heat equation |
| Keyword:
|
global solution |
| Keyword:
|
stochastic completeness |
| Keyword:
|
porous-media equation |
| Keyword:
|
McKean type estimate |
| MSC:
|
05C50 |
| MSC:
|
35Jxx |
| MSC:
|
53Cxx |
| MSC:
|
58J35 |
| MSC:
|
68R10 |
| idZBL:
|
Zbl 07584089 |
| idMR:
|
MR4483052 |
| DOI:
|
10.5817/AM2022-3-177 |
| . |
| Date available:
|
2022-09-01T10:20:55Z |
| Last updated:
|
2023-03-13 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/150663 |
| . |
| Reference:
|
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| . |
