Dissipation in Parabolic SPDEs

Dissipation in Parabolic SPDEs

The study of intermittency for the parabolic Anderson problem usually focuses on the moments of the solution which can describe the high peaks in the probability space. In this paper we set up the equation on a finite spatial interval, and study the other part of intermittency, i.e., the part of the...

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Veröffentlicht in:Journal of statistical physics 2020-04, Vol.179 (2), p.502-534
Hauptverfasser: Khoshnevisan, Davar, Kim, Kunwoo, Mueller, Carl, Shiu, Shang-Yuan
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Intermittency
Mathematical and Computational Physics
Physical Chemistry
Physics
Physics and Astronomy
Quantum Physics
Statistical Physics and Dynamical Systems
Theoretical
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container_title Journal of statistical physics
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creator Khoshnevisan, Davar
Kim, Kunwoo
Mueller, Carl
Shiu, Shang-Yuan
description The study of intermittency for the parabolic Anderson problem usually focuses on the moments of the solution which can describe the high peaks in the probability space. In this paper we set up the equation on a finite spatial interval, and study the other part of intermittency, i.e., the part of the probability space on which the solution is close to zero. This set has probability very close to one, and we show that on this set, the supremum of the solution over space is close to 0. As a consequence, we find that almost surely the spatial supremum of the solution tends to zero exponentially fast as time increases. We also show that if the noise term is very large, then the probability of the set on which the supremum of the solution is very small has a very high probability.
doi_str_mv 10.1007/s10955-020-02540-0
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subjects Intermittency
Mathematical and Computational Physics
Physical Chemistry
Physics
Physics and Astronomy
Quantum Physics
Statistical Physics and Dynamical Systems
Theoretical
title Dissipation in Parabolic SPDEs
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