Porous media equation on locally finite graphs

Li Ma

Archivum Mathematicum (2022)

  • Volume: 058, Issue: 3, page 177-187
  • ISSN: 0044-8753

Abstract

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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.

How to cite

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Ma, Li. "Porous media equation on locally finite graphs." Archivum Mathematicum 058.3 (2022): 177-187. <http://eudml.org/doc/298334>.

@article{Ma2022,
abstract = {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.},
author = {Ma, Li},
journal = {Archivum Mathematicum},
keywords = {Bochner formula; heat equation; global solution; stochastic completeness; porous-media equation; McKean type estimate},
language = {eng},
number = {3},
pages = {177-187},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Porous media equation on locally finite graphs},
url = {http://eudml.org/doc/298334},
volume = {058},
year = {2022},
}

TY - JOUR
AU - Ma, Li
TI - Porous media equation on locally finite graphs
JO - Archivum Mathematicum
PY - 2022
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 058
IS - 3
SP - 177
EP - 187
AB - 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.
LA - eng
KW - Bochner formula; heat equation; global solution; stochastic completeness; porous-media equation; McKean type estimate
UR - http://eudml.org/doc/298334
ER -

References

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