On a mixed fractional Burgers type equation with polynomial nonlinearity and perturbed by fractional Brownian sheet

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.

KEYWORDS:

• Fixed point theorem
• fractional Brownian sheet
• Hurst parameter
• mixed fractional Laplacian operators
• polynomial nonlinearity
• stochastic Burgers equation

AMS 2010 SUBJECT CLASSIFICATIONS:

• Primary: 60H15
• 60G22
• Secondary: 35Q35
• 35R60