Behavior of the solution of a random semilinear heat equation |
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| Authors: | S R S Varadhan Nikos Zygouras |
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| Institution: | 1. Courant Institute, 251 Mercer Street, New York, NY 10012‐1185;2. University of Southern California, Department of Mathematics, 3620 Vermont Avenue, KAP 108, Los Angeles, CA 90089‐2532 |
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| Abstract: | We consider a semilinear heat equation in one space dimension, with a random source at the origin. We study the solution, which describes the equilibrium of this system, and prove that, as the space variable tends to infinity, the solution becomes a.s. asymptotic to a steady state. We also study the fluctuations of the solution around the steady state. |
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