On degenerate coupled transport processes in porous media with memory phenomena

TL;DR

This paper establishes the existence of weak solutions for complex coupled transport systems in porous media with memory effects, addressing degeneracies in nonlinear coefficients through advanced mathematical techniques.

Contribution

It proves the existence of global weak solutions for degenerate coupled transport equations in porous media with memory, using semidiscretization and De Giorgi-Moser iteration methods.

Findings

Existence of weak solutions under physically relevant boundary conditions.

Handling of degeneracies in nonlinear transport coefficients.

Application of advanced iterative techniques for a-priori estimates.

Abstract

In this paper we prove the existence of weak solutions to degenerate parabolic systems arising from the fully coupled moisture movement, solute transport of dissolved species and heat transfer through porous materials. Physically relevant 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, proving necessary uniform estimates 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 transport coefficients are overcome by proving suitable a-priori $L^{\infty}$-estimates based on De Giorgi and Moser iteration technique.