Single-point blow-up for a semilinear parabolic system

• Autores: Philippe Souplet
• Localización: Journal of the European Mathematical Society, ISSN 1435-9855, Vol. 11, Nº 1, 2009, págs. 169-188
• Idioma: inglés
• DOI: 10.4171/jems/145
• Texto completo no disponible (Saber más ...)
• Resumen

  • 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