Decay Estimates for Solutions of Porous Medium Equations with Advection
Analysis of PDEs
2019-03-14 v3
Abstract
In this paper, we show that bounded weak solutions of the Cauchy problem for general degenerate parabolic equations of the form \begin{equation} \notag u_t \,+\; \mbox{div}\,f(x,t,u) \;=\; \mbox{div}\,(\;\!|\,u\,|^{\alpha} \, \nabla u \;\!), \quad \;\; x \in \mathbb{R}^{n}\!\:\!, \; t > 0, \end{equation} where is constant, decrease to zero, under fairly broad conditions on the advection flux . Besides that, we derive a time decay rate for these solutions.
Cite
@article{arxiv.1710.08959,
title = {Decay Estimates for Solutions of Porous Medium Equations with Advection},
author = {Nicolau Matiel Lunardi Diehl and Lucineia Fabris and Juliana Sartori Ziebell},
journal= {arXiv preprint arXiv:1710.08959},
year = {2019}
}