Sharp Transition Between Extinction and Propagation of Reaction
| dc.creator | Zlatos, Andrej | |
| dc.date | 2005-04-15 | |
| dc.date.accessioned | 2026-07-07T05:19:09Z | |
| dc.date.available | 2026-07-07T05:19:09Z | |
| dc.description | We consider the reaction-diffusion equation \[ T_t = T_{xx} + f(T) \] on $\bbR$ with $T_0(x) \equiv χ_{[-L,L]} (x)$ and $f(0)=f(1)=0$. In 1964 Kanel' proved that if $f$ is an ignition non-linearity, then $T\to 0$ as $t\to\infty$ when $L<L_0$, and $T\to 1$ when $L>L_1$. We answer the open question of relation of $L_0$ and $L_1$ by showing that $L_0=L_1$. We also determine the large time limit of $T$ in the critical case $L=L_0$, thus providing the phase portrait for the above PDE with respect to a 1-parameter family of initial data. Analogous results for combustion and bistable non-linearities are proved as well. | |
| dc.description | 15 pages | |
| dc.identifier | https://arxiv.org/abs/math/0504333 | |
| dc.identifier | http://arxiv.org/abs/math/0504333 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/74919 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 35K57, 35K15 | |
| dc.title | Sharp Transition Between Extinction and Propagation of Reaction | |
| dc.type | text |