Descret Solution for a Nonlinear Parabolic Equations with Diffusion Terms in Museilak-Spaces
Analysis of PDEs
2021-05-25 v1
Abstract
In this paper, we study a class of nonlinear evolution equations with damping arising in fluid dynamics and rheology. The nonlinear term is monotone and possesses a convex potential but exhibits non-standard growth. The appropriate functional framework for such equations is the modular Museilak-Spaces. We prove the existence and uniqueness of a weak solution using an approximation approach by combining an internal approximation with the backward Euler scheme, also a priori error estimate for the temporal semi-discretization is given.
Cite
@article{arxiv.2105.10600,
title = {Descret Solution for a Nonlinear Parabolic Equations with Diffusion Terms in Museilak-Spaces},
author = {A. Aberqi and M. Elmassoudi and M. Hammoumi},
journal= {arXiv preprint arXiv:2105.10600},
year = {2021}
}