Homogenization of pseudoparabolic reaction-diffusion-mechanics systems : Multiscale modeling, well-posedness and convergence rates

Abstract: In this dissertation, parabolic-pseudoparabolic equations are proposed to couple chemical reactions, diffusion, flow and mechanics in heterogeneous materials using the framework of mixture theory. The weak solvability is obtained in a one dimensional setting for the full system posed in a homogeneous domain - a formulation which we have obtained using the classical mixture theory. To give a glimpse of what each component of the system does, we illustrate numerically that approximate solutions according to the Rothe method exhibit realistic behaviour in suitable parameter regimes. The periodic homogenization in higher space dimensions is performed for a particular case of the initial system of partial differential equations posed in perforated domains. Besides obtaining upscaled model equations and formulas for computing effective transport coefficients, we also derive corrector/convergence estimates which delimitate the precision of the upscaling procedure. Finally, the periodic homogenization is performed for a thin vanishing multidomain. Corrector estimates are obtained for a comb-like domain placed on a thin plate in a monotone operator setting for pseudoparabolic equations.