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

2012/11/05 by Rossitza Semerdjieva, Semerdjieva, Rossitza
Engineering · Mathematics · #35K10 #35R35 #45G15 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1211.0894

openalex publication_date 2012/11/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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