Geodesic
Single-point blow-up for a semilinear parabolic system
Journal of the European Mathematical Society, Tome 11 (2009) no. 1, pp. 169-188 Cet article a éte moissonné depuis la source EMS Press

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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.
DOI : 10.4171/jems/145
Classification : 35-XX, 00-XX
Keywords: Semilinear parabolic system, reaction-diffusion, power nonlinearities, blow-up set, single point blow-up 
@article{JEMS_2009_11_1_a2,
     author = {Philippe Souplet},
     title = {Single-point blow-up for a semilinear parabolic system},
     journal = {Journal of the European Mathematical Society},
     pages = {169--188},
     year = {2009},
     volume = {11},
     number = {1},
     doi = {10.4171/jems/145},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/145/}
}
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Philippe Souplet. Single-point blow-up for a semilinear parabolic system. Journal of the European Mathematical Society, Tome 11 (2009) no. 1, pp. 169-188. doi: 10.4171/jems/145

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