Large-time behavior for viscous and non-viscous Hamilton-Jacobi equations forced by additive noise
Nicolas Dirr and Panagiotis E. Souganidis
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Submission date: 23. Aug. 2004 (revised version: November 2005)
published in: SIAM journal on mathematical analysis, 37 (2005) 3, p. 777-796
DOI number (of the published article): 10.1137/040611896
MSC-Numbers: 35R60, 49L25, 35B40
Keywords and phrases: hamilton-jacobi equations, pde with stochastic forcing, lipschitz regularity of hamilton-jacobi equations
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We study the large time behavior of the solutions to viscous and non-viscous Hamilton-Jacobi equations with additive noise and periodic spatial dependence. Under general structural conditions on the Hamiltonian, we show the existence of unique up to constants global in time solutions, which attract any other solution.