The paper is concerned with the heat equation perturbed by a spatially homogeneous Wiener process. It is shown, under general conditions on the spectral density of the noise, that solutions starting from non-negative initial conditions are strictly positive for all positive times. The result has an application to the existence of a stationary solution to a stochastic Burgers equation in dimensions higher than 2
Tessitore, G., Zabczyk, J. (1998). Strict positivity for stochastic heat equations 1. STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 77(1), 83-98 [10.1016/S0304-4149(98)00024-6].
Strict positivity for stochastic heat equations 1
Tessitore, G;
1998
Abstract
The paper is concerned with the heat equation perturbed by a spatially homogeneous Wiener process. It is shown, under general conditions on the spectral density of the noise, that solutions starting from non-negative initial conditions are strictly positive for all positive times. The result has an application to the existence of a stationary solution to a stochastic Burgers equation in dimensions higher than 2
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