Lattice approximation for stochastic reaction diffusion equations with one-sided Lipschitz condition

Sauer, Martin; Stannat, Wilhelm

doi:10.1090/S0025-5718-2014-02873-1

Lattice approximation for stochastic reaction diffusion equations with one-sided Lipschitz condition
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by Martin Sauer and Wilhelm Stannat PDF

Math. Comp. 84 (2015), 743-766 Request permission

Abstract:

We consider strong convergence of the finite differences approximation in space for stochastic reaction diffusion equations in one dimension with multiplicative noise under a one-sided Lipschitz condition only. The equation may be additionally coupled with a noisy control variable with global Lipschitz condition but no diffusion. We derive convergence with an implicit rate depending on the regularity of the exact solution. This can be made explicit if the variational solution has more than its canonical spatial regularity. As an application, spatially extended FitzHugh-Nagumo systems with noise are considered.

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