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arXiv · 1502.06633

Weak solutions to Allen-Cahn-like equations modelling consolidation of porous media

P. Artale Harris·E. N. M. Cirillo·A. Muntean
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Abstract

We study the weak solvability of a system of coupled Allen-Cahn-like equations resembling cross-diffusion which is arising as a model for the consolidation of saturated porous media. Besides using energy like estimates, we cast the special structure of the system in the framework of the Leray-Schauder fixed point principle and ensure this way the local existence of strong solutions to a regularised version of our system. Furthermore, weak convergence techniques ensure the existence of weak solutions to the original consolidation problem. The uniqueness of global-in-time solutions is guaranteed in a particular case. Moreover, we use a finite difference scheme to show the negativity of the vector of solutions.

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P. Artale Harris, E. N. M. Cirillo, A. Muntean. 2015-02-23. Weak solutions to Allen-Cahn-like equations modelling consolidation of porous media. https://arxiv.org/abs/1502.06633

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