Uniqueness of Degenerating Solutions to a Diffusion-Precipitation Model for Clogging Porous Media

Abstract

The current article presents a degenerating diffusion-precipitation model including vanishing porosity and focuses primarily on uniqueness results. This is accomplished by assuming sufficient conditions under which the uniqueness of weak solutions can be established. Moreover, a proof of existence based on a compactness argument yields rather regular solutions, satisfying these unique conditions. The results show that every strong solution is unique, though a slightly different condition is additionally required in three dimensions. The analysis presents particular challenges due to the nonlinear structure of the underlying problem and the necessity to work with appropriate weights and manage possible degeneration.