Lattice Approximation for Stochastic Reaction Diffusion Equations with One-Sided Lipschitz Condition
Probability
2015-04-17 v3
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.
Keywords
Cite
@article{arxiv.1301.6350,
title = {Lattice Approximation for Stochastic Reaction Diffusion Equations with One-Sided Lipschitz Condition},
author = {Martin Sauer and Wilhelm Stannat},
journal= {arXiv preprint arXiv:1301.6350},
year = {2015}
}
Comments
24 pages, 1 figure. This is the prepublication draft of the article published online in Math. Comp. (2014)