Uniqueness of Solution of the Unsteady Filtration Problem in Heterogeneous Porous Media

TL;DR

This paper proves the uniqueness of solutions for the unsteady dam problem in heterogeneous porous media, under specific boundary conditions, ensuring the model's reliability for such physical scenarios.

Contribution

It establishes the first rigorous proof of solution uniqueness for the unsteady filtration problem in heterogeneous media with particular boundary assumptions.

Findings

Uniqueness of solution is proven for the unsteady dam problem in heterogeneous media.

The proof applies to rectangular domains with specific wetting conditions.

Results ensure the mathematical well-posedness of the model under studied conditions.

Abstract

We establish uniqueness of the solution of the unsteady state dam problem in the heterogeneous and rectangular case assuming the dam wet at the bottom and dry near to the top.