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

Nicolas Fournier (1) , Jacques Printems (1)

1 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées

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.

Domaines: Physique mathématique [math-ph]

Nicolas Fournier, Jacques Printems. STABILITY OF THE STOCHASTIC HEAT EQUATION IN L(1)([0,1]). Electronic Communications in Probability, 2011, 16, pp.337-352. ⟨10.1214/ECP.v16-1636⟩. ⟨hal-00692984⟩