Strong solutions of semilinear matched microstructure models

Joachim Escher; Daniela Treutler

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arXiv · 1112.4278

Strong solutions of semilinear matched microstructure models

Joachim Escher·Daniela Treutler

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Abstract

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.

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Joachim Escher, Daniela Treutler. 2011-12-20. Strong solutions of semilinear matched microstructure models. https://arxiv.org/abs/1112.4278

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