Existence of weak solutions for a pseudo-parabolic system coupling chemical reactions, diffusion and momentum equations
Arthur J. Vromans, Alfons A. F. van de Ven, Adrian Muntean · arXiv (Cornell University) · 2017
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.