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arXiv · 2512.09298

On the elasto-plastic filtration equation

Arturo de Pablo·Fernando Quiros·Julio D. Rossi
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Abstract

We study the fully nonlinear heat equation $b(\partial_tu)\partial_tu=\Delta u$ posed in a bounded domain with Dirichlet boundary conditions. Here $b(s)=b^-$ if $s<0$, $b(s)=b^+$ if $s>0$, $b^-\neq b^+$ being two positive constants. This equation models the flow of an elastic fluid in an elasto-plastic porous medium. We are interested in the existence and uniqueness of viscosity solutions and in their asymptotic behaviour as $t\to\infty$ and when $b^-\to 0^+$ or $b^+\to +\infty$. We also characterize solutions of the problem as limits of a minimization dynamic game.

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Arturo de Pablo, Fernando Quiros, Julio D. Rossi. 2025-12-10. On the elasto-plastic filtration equation. https://arxiv.org/abs/2512.09298

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