2011/12/19 by Joachim Escher, Escher, Joachim, Daniela Treutler +1
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Analysis of PDEs (math.AP) #Composite Material Mechanics #FOS: Mathematics #math.AP
paper · pdf · doi:10.48550/arxiv.1112.4278
openalex publication_date 2011/12/19 · arxiv created 2011/12/20 · arxiv updated 2011/12/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The subject of this article is a matched microstructure model for Newtonian fluid flows in fractured porous media. This is a homogenized model which takes the form of two coupled parabolic differential equations with boundary conditions in a given (two-scale) domain in Euclidean space. The main objective is to establish the local well-posedness in the strong sense of the flow. Two main settings are investigated: semi-linear systems with linear boundary conditions and semi-linear systems with nonlinear boundary conditions. With the help of analytic semigoups we establish local well-posedness and investigate the long-time behaviour of the solutions in the first case: we establish global existence and show that solutions converge to zero at an exponential rate.