On some properties of entropy solutions of degenerate non-linear anisotropic parabolic equations
Analysis of PDEs
2020-04-20 v1
Abstract
We prove existence of the largest and the smallest entropy solutions to the Cauchy problem for a nonlinear degenerate anisotropic parabolic equation. Applying this result, we establish the comparison principle in the case when at least one of the initial functions is periodic. In the case when initial function vanishes at infinity (in the sense of strong average) we prove the long time decay of an entropy solution under exact nonlinearity-diffusivity condition.
Keywords
Cite
@article{arxiv.2004.07830,
title = {On some properties of entropy solutions of degenerate non-linear anisotropic parabolic equations},
author = {Evgeny Yu. Panov},
journal= {arXiv preprint arXiv:2004.07830},
year = {2020}
}
Comments
arXiv admin note: text overlap with arXiv:1904.01370, arXiv:1910.08739