Regularity and long time behavior of a doubly nonlinear parabolic problem and its discretization
Analysis of PDEs
2023-05-31 v1
Abstract
We study a doubly nonlinear parabolic problem arising in the modeling of gas transport in pipelines. Using convexity arguments and relative entropy estimates we show uniform bounds and exponential stability of discrete approximations obtained by a finite element method and implicit time stepping. Due to convergence of the approximations to weak solutions of the problem, our results also imply regularity, uniqueness, and long time stability of weak solutions of the continuous problem.
Keywords
Cite
@article{arxiv.2305.18886,
title = {Regularity and long time behavior of a doubly nonlinear parabolic problem and its discretization},
author = {Herbert Egger and Jan Giesselmann},
journal= {arXiv preprint arXiv:2305.18886},
year = {2023}
}