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Keywords:
Bochner formula; heat equation; global solution; stochastic completeness; porous-media equation; McKean type estimate
Bochner formula; heat equation; global solution; stochastic completeness; porous-media equation; McKean type estimate
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.
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