Lattice Approximation for Stochastic Reaction Diffusion Equations with One-Sided Lipschitz Condition

Martin Sauer; Wilhelm Stannat

doi:10.1090/s0025-5718-2014-02873-1

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arXiv · 1301.6350

Lattice Approximation for Stochastic Reaction Diffusion Equations with One-Sided Lipschitz Condition

Martin Sauer·Wilhelm Stannat

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Abstract

We consider strong convergence of the finite differences approximation in space for stochastic reaction diffusion equations with multiplicative noise under a one-sided Lipschitz condition only. 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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BibTeX RIS

Martin Sauer, Wilhelm Stannat. 2013-01-27. Lattice Approximation for Stochastic Reaction Diffusion Equations with One-Sided Lipschitz Condition. https://doi.org/10.1090/s0025-5718-2014-02873-1

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