Global existence of classical solutions for a nonlocal one dimensional parabolic free boundary problem

TL;DR

This paper proves the global existence and uniqueness of classical solutions for a one-dimensional parabolic free boundary problem with nonlocal conditions, using integral equation analysis.

Contribution

It introduces a novel approach analyzing an equivalent system of nonlinear integral equations to establish solution existence and uniqueness.

Findings

Global classical solutions are proven to exist and be unique.

The method applies to problems with smooth initial-boundary data and compatibility conditions.

The approach offers a new perspective for nonlocal free boundary problems.

Abstract

In this paper we study one dimensional parabolic free boundary value problem with a nonlocal (integro-differential) condition on the free boundary. We establish global existence-uniqueness of classical solutions assuming that the initial-boundary data are sufficiently smooth and satisfy some compatibility conditions. Our approach is based on analysis of an equivalent system of nonlinear integral equations.