Construction of a stable blow-up solution for a class of strongly   perturbed semilinear heat equations
  We construct a solution for a class of strongly perturbed semilinear heat equations which blows up in finite time with a prescribed blow-up profile. The construction relies on the reduction of the problem to a finite dimensional one and the use of index theory to conclude. 
Van Tien Nguyen and Hatem Zaag
math.AP