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arXiv · 1209.1840

A note on stochastic semilinear equations and their associated Fokker-Planck equations

Michael Röckner·Rongchan Zhu·Xiangchan Zhu
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Abstract

In this paper we treat semilinear stochastic partial differential equations by two methods. First, we extend the framework of [BDR10] from a Hilbert space to a Gelfand triple and as an application we prove the existence of solutions for the Fokker-Planck equations associated to semilinear equations with space-time white noise and both with polynomially growing nonlinearities and Burgers type nonlinearities at the same time. Second we adopt the approximation technique from [BDR10] to obtain existence of unique strong solutions to semilinear stochastic partial differential equations driven by space-time white noise, generalizing corresponding known results from the literature.

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Michael Röckner, Rongchan Zhu, Xiangchan Zhu. 2014-02-03. A note on stochastic semilinear equations and their associated Fokker-Planck equations. https://arxiv.org/abs/1209.1840

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