JournalsjemsVol. 11 , No. 1DOI 10.4171/jems/145

Single-point blow-up for a semilinear parabolic system

  • Philippe Souplet

    Université de Paris XIII, Villetaneuse, France
Single-point blow-up for a semilinear parabolic system cover

Abstract

We consider positive solutions of a semilinear parabolic system coupled by power nonlinearities, in a ball or in the whole space. Relatively little is known on the blow-up set for parabolic systems and, up to now, no result was available for this basic system except for the very special case of equal powers. Here we prove single-point blow-up for a large class of radial decreasing solutions. This in particular solves a problem left open in a paper of A.~Friedman and Y.~Giga (1987). We also obtain lower pointwise estimates for the final blow-up profiles.