Harnack inequalities for a class of semilinear stochastic partial differential equations
Harnack inequalities for a class of semilinear stochastic partial differential equations
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发表时间：
2018-07
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通讯作者：
Rangrang Zhang
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作者：
Rangrang Zhang
本文研究了一类由时空加性白色噪声驱动的半线性随机偏微分方程。利用耦合方法建立了与解相联系的半群的Harnack不等式，该不等式蕴含强Feller性质。我们的结果推广了Zhang [Potential Analysis 33（2010），no. 2，137-151.]并可应用于受时空白色噪声扰动的反应扩散方程和输运扩散方程。
In this article, we study a class of semilinear stochastic partial differential equations driven by an additive space time white noise. We establish Harnack inequalities for the semigroup associated with the solution by using coupling method, which implies the strong Feller property. Our results generalize the results of Zhang [Potential Analysis 33 (2010), no. 2, 137-151.] and can be applied to some types of SPDE such as reaction-diffusion equation and transport-diffusion equation perturbed by space time white noise.