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STABILITY OF THE STOCHASTIC HEAT EQUATION IN L(1)([0,1])

Abstract : We consider the white-noise driven stochastic heat equation on [0, infinity) x [0, 1] with Lipschitz-continuous drift and diffusion coefficients. We derive an inequality for the L(1)([0, 1])-norm of the difference between two solutions. Using some martingale arguments, we show that this inequality provides some estimates which allow us to study the stability of the solution with respect the initial condition, the uniqueness of the possible invariant distribution and the asymptotic confluence of solutions.
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https://hal-upec-upem.archives-ouvertes.fr/hal-00692984
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Submitted on : Tuesday, May 1, 2012 - 7:13:31 PM
Last modification on : Thursday, March 19, 2020 - 12:26:02 PM

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  • HAL Id : hal-00692984, version 1

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Nicolas Fournier, Jacques Printems. STABILITY OF THE STOCHASTIC HEAT EQUATION IN L(1)([0,1]). Electronic Communications in Probability, Institute of Mathematical Statistics (IMS), 2011, 16 (?), pp.337--352. ⟨hal-00692984⟩

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