Global existence of classical solutions for a nonlocal one dimensional   parabolic free boundary problem
  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. 
Rossitza Semerdjieva
math.AP