Global weak solutions to degenerate coupled diffusion-convection-dispersion processes and heat transport in porous media

TL;DR

This paper proves the existence of global weak solutions for complex degenerate coupled diffusion, convection, and heat transfer systems in porous media, addressing mathematical challenges posed by degeneracies in transport coefficients.

Contribution

It introduces a novel approach to establish existence of solutions for degenerate coupled systems with physically motivated boundary conditions, overcoming degeneracies without boundedness assumptions.

Findings

Existence of global weak solutions is established.

Degeneracies in transport coefficients are managed via new a-priori estimates.

The method applies to physically relevant porous media models.

Abstract

In this contribution we prove the existence of weak solutions to degenerate parabolic systems arising from the coupled moisture movement, transport of dissolved species and heat transfer through partially saturated porous materials. Physically motivated mixed Dirichlet-Neumann boundary conditions and initial conditions are considered. Existence of a global weak solution of the problem is proved by means of semidiscretization in time and by passing to the limit from discrete approximations. Degeneration occurs in the nonlinear transport coefficients which are not assumed to be bounded below and above by positive constants. Degeneracies in all transport coefficients are overcome by proving suitable a-priori $L^{\infty}$-estimates for the approximations of primary unknowns of the system.