# Single-point blow-up for a semilinear parabolic system

Journal of the European Mathematical Society (2009)

- Volume: 011, Issue: 1, page 169-188
- ISSN: 1435-9855

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topSouplet, 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 -

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