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

2017/02/08 by Arthur J. Vromans, Vromans, Arthur J., A.A.F. van de Ven +3 · 1 citation
Computer Science · Mathematics · #35A01 #35K51 (Primary) 35D30 #35K70 #74D05 #74F10 #74F20 #74F25 (Secondary) #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.1702.02481

openalex publication_date 2017/02/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Citations

• Sharp Interface Limit for a Stokes/Allen-Cahn System

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