×

zbMATH — the first resource for mathematics

Well posedness and asymptotic behavior for stochastic reaction-diffusion equations with multiplicative Poisson noise. (English) Zbl 1225.60108
Summary: We establish well-posedness in the mild sense for a class of stochastic semilinear evolution equations with a polynomially growing quasi-monotone nonlinearity and multiplicative Poisson noise. We also study the existence and uniqueness of invariant measures for the associated semigroup in the Markovian case. A key role is played by a new maximal inequality for stochastic convolutions in \(L_p\) spaces.

MSC:
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
60G57 Random measures
PDF BibTeX XML Cite
Full Text: DOI EMIS