Geodesic
Porous media equation on locally finite graphs
Archivum mathematicum, Tome 58 (2022) no. 3, pp. 177-187 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
DOI : 10.5817/AM2022-3-177
Classification : 05C50, 35Jxx, 53Cxx, 58J35, 68R10
Keywords: Bochner formula; heat equation; global solution; stochastic completeness; porous-media equation; McKean type estimate 
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Ma, Li. Porous media equation on locally finite graphs. Archivum mathematicum, Tome 58 (2022) no. 3, pp. 177-187. doi: 10.5817/AM2022-3-177

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