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In this paper we study one dimensional parabolic free boundary value problemwith a nonlocal (integro-differential) condition on the free boundary. Weestablish global existence-uniqueness of classical solutions assuming that theinitial-boundary data are sufficiently smooth and satisfy some compatibilityconditions. Our approach is based on analysis of an equivalent system ofnonlinear integral equations.

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