Intermittence and nonlinear parabolic stochastic partial differential equations
| dc.creator | Foondun, Mohammud | |
| dc.creator | Khoshnevisan, Davar | |
| dc.date | 2008-05-05 | |
| dc.date.accessioned | 2026-07-07T09:37:04Z | |
| dc.date.available | 2026-07-07T09:37:04Z | |
| dc.description | We consider nonlinear parabolic SPDEs of the form $\partial_t u=\sL u + σ(u)\dot w$, where $\dot w$ denotes space-time white noise, $σ:\R\to\R$ is [globally] Lipschitz continuous, and $\sL$ is the $L^2$-generator of a Lévy process. We present precise criteria for existence as well as uniqueness of solutions. More significantly, we prove that these solutions grow in time with at most a precise exponential rate. We establish also that when $σ$ is globally Lipschitz and asymptotically sublinear, the solution to the nonlinear heat equation is ``weakly intermittent,'' provided that the symmetrization of $\sL$ is recurrent and the initial data is sufficiently large. Among other things, our results lead to general formulas for the upper second-moment Liapounov exponent of the parabolic Anderson model for $\sL$ in dimension $(1+1)$. When $\sL=κ\partial_{xx}$ for $κ>0$, these formulas agree with the earlier results of statistical physics \cite{Kardar,KrugSpohn,LL63}, and also probability theory \cite{BC,CM94} in the two exactly-solvable cases where $u_0=δ_0$ and $u_0\equiv 1$. | |
| dc.identifier | https://arxiv.org/abs/0805.0557 | |
| dc.identifier | http://arxiv.org/abs/0805.0557 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/160334 | |
| dc.subject | Probability | |
| dc.subject | 60H15; 82B44 | |
| dc.title | Intermittence and nonlinear parabolic stochastic partial differential equations | |
| dc.type | text |