Name
Abstract | ||
|---|---|---|
A system of semilinear parabolic stochastic partial differential equations with additive space-time noise is considered on the union of thin bounded tubular domains D-1,D-epsilon := Gamma x (0, epsilon) and D-2,D-epsilon := Gamma x (-epsilon, 0) joined at the common base Gamma subset of R-d, where d >= 1. The equations are coupled by an interface condition on Gamma which involves a reaction intensity k(x', epsilon), where x = (x' , x(d+1)) is an element of Rd+1 with x' is an element of Gamma and |x(d+1)| < epsilon. Random influences are included through additive space-time Brownian motion, which depend only on the base spatial variable x' is an element of G and not on the spatial variable x(d+1) in the thin direction. Moreover, the noise is the same in both layers D-1,D-epsilon and D-2,D- epsilon. Limiting properties of the global random attractor are established as the thinness parameter of the domain epsilon -> 0, i.e., as the initial domain becomes thinner, when the intensity function possesses the property lim(epsilon -> 0) epsilon(-1)k(x', epsilon) = +infinity. In particular, the limiting dynamics is described by a single stochastic parabolic equation with the averaged di. usion coe. cient and a nonlinearity term, which essentially indicates synchronization of the dynamics on both sides of the common base Gamma. Moreover, in the case of nondegenerate noise we obtain stronger synchronization phenomena in comparison with analogous results in the deterministic case previously investigated by Chueshov and Rekalo [EQUADIFF-2003, F. Dumortier et al., eds., World Scienti. c, Hackensack, NJ, 2005, pp. 645-650; Sb. Math., 195 (2004), pp. 103-128]. |
Year | DOI | Venue |
|---|---|---|
2006 | 10.1137/050647281 | SIAM JOURNAL ON MATHEMATICAL ANALYSIS |
Keywords | Field | DocType |
thin domains,random attractors,synchronization | Attractor,Mathematical analysis,Stochastic partial differential equation,Brownian motion,Partial differential equation,Reaction–diffusion system,Diffusion equation,Mathematics,Parabola,Bounded function | Journal |
Volume | Issue | ISSN |
38 | 5 | 0036-1410 |
Citations | PageRank | References |
0 | 0.34 | 0 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Tomás Caraballo | 1 | 39 | 16.55 |
| Igor Chueshov | 2 | 0 | 1.01 |
| Peter E. Kloeden | 3 | 87 | 21.04 |