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

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  • Voß-Böhme, Anja

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

Suggested Citation

  • Voß-Böhme, Anja, 2003. "Asymptotic mass distribution speed for the one-dimensional heat equation with constant drift and stationary potential," Stochastic Processes and their Applications, Elsevier, vol. 106(2), pages 167-184, August.
    • Handle: RePEc:eee:spapps:v:106:y:2003:i:2:p:167-184
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