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Parameter delimitation of the weak solvability for a pseudo-parabolic system coupling chemical reactions, diffusion and momentum equations. (English) Zbl 1470.35132

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.

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
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