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

TL;DR

This paper proves the existence of weak solutions for a complex coupled system of equations modeling mechanics, chemical reactions, diffusion, and flow, using energy estimates and the Rothe method.

Contribution

It establishes the weak solvability of a nonlinear pseudo-parabolic system with a novel approach based on discrete energy estimates and convergence analysis.

Findings

Weak solutions exist under certain parameter regimes.

The Rothe method converges for the discretized system.

Energy estimates ensure stability and convergence.

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.