Stochastic Reaction-diffusion Equations Driven by Jump Processes

Abstract

We establish the existence of weak martingale solutions to a class of second order parabolic stochastic partial differential equations. The equations are driven by multiplicative jump type noise, with a non-Lipschitz multiplicative functional. The drift in the equations contains a dissipative nonlinearity of polynomial growth.

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References in corpus (5)

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• Itô isomorphisms for $L^p$-valued Poisson stochastic integrals
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• Global well-posedness to stochastic reaction-diffusion equations on the real line $\mathbb{R}$ with superlinear drifts driven by multiplicative space-time white noise
• Existence of weak solutions to stochastic heat equations driven by truncated $\alpha$-stable white noises with non-Lipschitz coefficients
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• Existence of a martingale solution of the stochastic Hall-MHD equations perturbed by Poisson type random forces on ${\mathbb{R}}^3$
• Stochastic 2D Navier-Stokes equations on time-dependent domains
• Stochastic optimal control of a evolutionary $p$-Laplace equation with multiplicative Lévy noise
• The first exit problem of reaction-diffusion equations for small multiplicative Lévy noise
• Martingale solution, invariant measure and ergodicity for stochastic convective Brinkman-Forchheimer equations on general domains in ${\mathbb{R}}^d$