Solution of a nonlinear heat equation with arbitrarily given blow‐up points

Source abstract

Abstract We consider the equation where I ⊂ ℝ u is scalar‐valued and p > 1. It has been proven that if u(t) blows up at time T , the blow‐up points are finite in number and located in I °. Our aim is to prove that this result is optimal. That is, for any given points x 1 ,…, x k in I ° there is a solution u such that its blow‐up points are exactly x 1 ,…, x k .