Existence of weak solutions for general nonlocal and nonlinear   second-order parabolic equations
  In this article, we provide existence results for a general class of nonlocal and nonlinear second-order parabolic equations. The main motivation comes from front propagation theory in the cases when the normal velocity depends on the moving front in a nonlocal way. Among applications, we present level-set equations appearing in dislocations' theory and in the study of Fitzhugh-Nagumo systems. 
Guy Barles (LMPT), Pierre Cardaliaguet (LM-Brest), Olivier Ley (LMPT),   Aur\'elien Monteillet (LM-Brest)