Asymptotic mass distribution speed for the one-dimensional heat equation with constant drift and stationary potential

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:106

Article

Voss-Böhme, A

关键词: heat equation with constant drift and stationary potential;    random media;    random environment;    large deviations;    quenched behavior;    Wiener process with drift under exponentially weighted path measure;   

DOI  :  10.1016/S0304-4149(03)00047-4

来源: Elsevier

【 摘 要 】

We study the long-time behavior of the solution u(t,x) of a Cauchy problem for the one-dimensional heat equation with constant drift and random potential in the quenched setting: u(t) = 1/2u(xx) + hu(x) + xiu. The initial function is compactly supported. For bounded stationary ergodic potential xi, we show that u is asymptotically (t --> infinity) concentrated in a ball of radius o(t) and center nu(h)t which is independent of the realization of the random potential. There is a critical drift value h(cr) where we observe a change from sublinear (nu(h) = 0) to linear (0 < nu(h) less than or equal to h) mass propagation. (C) 2003 Elsevier Science B.V. All rights reserved.

【 授权许可】

Free