# Transition from decay to blow-up in a parabolic system

Archivum Mathematicum (1998)

- Volume: 034, Issue: 1, page 199-206
- ISSN: 0044-8753

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topQuittner, Pavol. "Transition from decay to blow-up in a parabolic system." Archivum Mathematicum 034.1 (1998): 199-206. <http://eudml.org/doc/18528>.

@article{Quittner1998,

abstract = {We show a locally uniform bound for global nonnegative solutions of the system $u_t=\Delta u+uv-bu$, $v_t=\Delta v+au$ in $(0,+\infty )\times \Omega $, $u=v=0$ on $(0,+\infty )\times \partial \Omega $, where $a>0$, $b\ge 0$ and $\Omega $ is a bounded domain in $\mathbb \{R\}^n$, $n\le 2$. In particular, the trajectories starting on the boundary of the domain of attraction of the zero solution are global and bounded.},

author = {Quittner, Pavol},

journal = {Archivum Mathematicum},

keywords = {Blow-up; global existence; apriori estimates; domain of attraction of the zero solution; global existence; a priori estimates},

language = {eng},

number = {1},

pages = {199-206},

publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},

title = {Transition from decay to blow-up in a parabolic system},

url = {http://eudml.org/doc/18528},

volume = {034},

year = {1998},

}

TY - JOUR

AU - Quittner, Pavol

TI - Transition from decay to blow-up in a parabolic system

JO - Archivum Mathematicum

PY - 1998

PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno

VL - 034

IS - 1

SP - 199

EP - 206

AB - We show a locally uniform bound for global nonnegative solutions of the system $u_t=\Delta u+uv-bu$, $v_t=\Delta v+au$ in $(0,+\infty )\times \Omega $, $u=v=0$ on $(0,+\infty )\times \partial \Omega $, where $a>0$, $b\ge 0$ and $\Omega $ is a bounded domain in $\mathbb {R}^n$, $n\le 2$. In particular, the trajectories starting on the boundary of the domain of attraction of the zero solution are global and bounded.

LA - eng

KW - Blow-up; global existence; apriori estimates; domain of attraction of the zero solution; global existence; a priori estimates

UR - http://eudml.org/doc/18528

ER -

## References

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