Porous medium equation with a blow-up nonlinearity and a non-decreasing constraint
Analysis of PDEs
2018-02-28 v1
Abstract
The final goal of this paper is to prove existence of local (strong) solutions to a (fully nonlinear) porous medium equation with blow-up term and nondecreasing constraint. To this end, the equation, arising in the context of Damage Mechanics, is reformulated as a mixed form of two different types of doubly nonlinear evolution equations. Global (in time) solutions to some approximate problems are constructed by performing a time discretization argument and by taking advantage of energy techniques based on specific structures of the equation. Moreover, a variational comparison principle for (possibly non-unique) approximate solutions is established and it also enables us to obtain a local solution as a limit of approximate ones.
Keywords
Cite
@article{arxiv.1802.09570,
title = {Porous medium equation with a blow-up nonlinearity and a non-decreasing constraint},
author = {Goro Akagi and Stefano Melchionna},
journal= {arXiv preprint arXiv:1802.09570},
year = {2018}
}