Single-point blow-up for a semilinear parabolic system

Souplet, Ph.. "Single-point blow-up for a semilinear parabolic system." Journal of the European Mathematical Society 011.1 (2009): 169-188. <http://eudml.org/doc/277279>.

@article{Souplet2009,
abstract = {We consider positive solutions of the system $u_t-\Delta u=v^p$; $v_t-\Delta v=u^q$ in a ball or in the whole space, with $p,q>1$. Relatively little is known on the blow-up set for semilinear parabolic systems and, up to now, no result was available for this basic system except for the very special case $p=q$. 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.},
author = {Souplet, Ph.},
journal = {Journal of the European Mathematical Society},
keywords = {semilinear parabolic system; reaction-diffusion; power nonlinearities; blow-up set; single point blow-up; positive solutions; semilinear parabolic system; nonlinearities; blow-up set; single point blow-up},
language = {eng},
number = {1},
pages = {169-188},
publisher = {European Mathematical Society Publishing House},
title = {Single-point blow-up for a semilinear parabolic system},
url = {http://eudml.org/doc/277279},
volume = {011},
year = {2009},
}

TY - JOUR
AU - Souplet, Ph.
TI - Single-point blow-up for a semilinear parabolic system
JO - Journal of the European Mathematical Society
PY - 2009
PB - European Mathematical Society Publishing House
VL - 011
IS - 1
SP - 169
EP - 188
AB - We consider positive solutions of the system $u_t-\Delta u=v^p$; $v_t-\Delta v=u^q$ in a ball or in the whole space, with $p,q>1$. Relatively little is known on the blow-up set for semilinear parabolic systems and, up to now, no result was available for this basic system except for the very special case $p=q$. 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.
LA - eng
KW - semilinear parabolic system; reaction-diffusion; power nonlinearities; blow-up set; single point blow-up; positive solutions; semilinear parabolic system; nonlinearities; blow-up set; single point blow-up
UR - http://eudml.org/doc/277279
ER -