Local weak solvability of a moving boundary problem describing swelling along a halfline

TL;DR

This paper proves the local well-posedness of a moving boundary problem modeling water swelling in a pore, using advanced mathematical techniques to establish existence and uniqueness of solutions.

Contribution

It introduces a novel analysis combining a priori estimates, fixed point methods, and subdifferential evolution theory for this specific swelling problem.

Findings

Established local existence and uniqueness of solutions

Developed new a priori estimates for boundary evolution

Applied subdifferential evolution theory to boundary problems

Abstract

We obtain the local well-posedness of a moving boundary problem that describes the swelling of a pocket of water within an infinitely thin elongated pore. Our result involves fine a priori estimates of the moving boundary evolution, Banach fixed point arguments as well as an application of the general theory of evolution equations governed by subdifferentials.