Geodesic
Porous media equation on locally finite graphs
Archivum mathematicum, Tome 58 (2022) no. 3, pp. 177-187

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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.
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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