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

Anja Voß-Böhme

Stochastic Processes and their Applications, 2003, vol. 106, issue 2, 167-184

Abstract: 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: . 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 vht which is independent of the realization of the random potential. There is a critical drift value hcr where we observe a change from sublinear (vh=0) to linear (0

Keywords: 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 (search for similar items in EconPapers)
Date: 2003
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