Geodesic
Transition from decay to blow-up in a parabolic system
Archivum mathematicum, Tome 34 (1998) no. 1, pp. 199-206

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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.
Classification : 35B40, 35K50, 35K60
Keywords: Blow-up; global existence; apriori estimates 
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     author = {Quittner, Pavol},
     title = {Transition from decay to blow-up in a parabolic system},
     journal = {Archivum mathematicum},
     pages = {199--206},
     publisher = {mathdoc},
     volume = {34},
     number = {1},
     year = {1998},
     mrnumber = {1629705},
     zbl = {0911.35062},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ARM_1998__34_1_a18/}
}
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Quittner, Pavol. Transition from decay to blow-up in a parabolic system. Archivum mathematicum, Tome 34 (1998) no. 1, pp. 199-206. http://geodesic.mathdoc.fr/item/ARM_1998__34_1_a18/