Vromans, Arthur J.; van de Ven, Fons; Muntean, Adrian Parameter delimitation of the weak solvability for a pseudo-parabolic system coupling chemical reactions, diffusion and momentum equations. (English) Zbl 1470.35132 Adv. Math. Sci. Appl. 28, No. 2, 273-311 (2019). Summary: The weak solvability of a nonlinearly coupled system of parabolic and pseudo-parabolic equations describing the interplay between mechanics, chemical reactions, diffusion and flow modelled within a mixture theory framework is studied via energy-like estmiates and Gronwall inequalities. In analytically derived parameter regimes, these estimates ensure the convergence of discretized-in-time partial differential equations. These regimes are tested and extended numerically. Especially, the dependence of the temporal existence domain of physical behaviour on selected parameters is shown. Cited in 3 Documents MSC: 35D30 Weak solutions to PDEs 35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs 35K51 Initial-boundary value problems for second-order parabolic systems 35K55 Nonlinear parabolic equations 35K57 Reaction-diffusion equations 35K70 Ultraparabolic equations, pseudoparabolic equations, etc. 74D05 Linear constitutive equations for materials with memory 74F20 Mixture effects in solid mechanics Keywords:system of nonlinear parabolic and pseudo-parabolic equations; Rothe method PDFBibTeX XMLCite \textit{A. J. Vromans} et al., Adv. Math. Sci. Appl. 28, No. 2, 273--311 (2019; Zbl 1470.35132)