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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
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