Exponential convergence for a periodically driven semilinear heat equation |
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Authors: | Nikos Zygouras |
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Affiliation: | Department of Mathematics, University of Southern California, Los Angeles, CA 90089, USA |
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Abstract: | We consider a semilinear heat equation in one space dimension, with a periodic source at the origin. We study the solution, which describes the equilibrium of this system and we prove that, as the space variable tends to infinity, the solution becomes, exponentially fast, asymptotic to a steady state. The key to the proof of this result is a Harnack type inequality, which we obtain using probabilistic ideas. |
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Keywords: | 35K60 60H15 |
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