Abstract

In this paper, we discuss a class of stochastic nonlinear partial differential equation of Burgers type driven by pseudo differential operator $(\Delta +{\Delta }_{\alpha })$ for $\alpha \in (0,2),$ and fractional Brownian sheet. The existence and uniqueness of an L^p-valued (local) solution is established for the initial valued problem to the equation.

中文翻译：

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具有多项式非线性且受分数布朗片扰动的混合分数Burgers型方程

摘要

本文讨论了一类由伪微分算子驱动的Burgers型随机非线性偏微分方程 $(\Delta +{\Delta }_{\alpha })$ 为了 $\alpha \in (0,2),$和分数布朗表。为方程的初值问题建立了 L ^p值（局部）解的存在性和唯一性。