Existence of weak solutions for a pseudo-parabolic system coupling chemical reactions, diffusion and momentum equations

Abstract

We study the weak solvability of a nonlinearly coupled system of parabolic and pseudo-parabolic equations describing the interplay between mechanics, chemical reactions, diffusion and flow in a mixture theory framework. Our approach relies on suitable discrete-in-time energy-like estimates and discrete Gronwall inequalities. In selected parameter regimes, these estimates ensure the convergence of the Rothe method for the discretized partial differential equations.

35 pages, 0 figures, submitted to European Journal of Applied Mathematics on February 7th 2017

References in corpus (2)

• Homogenization of a Fully Coupled Thermoelasticity Problem for a Highly Heterogeneous Medium With a Priori Known Phase Transformations
• Sharp Interface Limit for a Stokes/Allen-Cahn System

Cited by in corpus (1)

• Homogenization of a pseudo-parabolic system via a spatial-temporal decoupling: upscaling and corrector estimates for perforated domains