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

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