| Volume 8, Number 1, 2018, Pages 202-228 DOI：10.11948/2018.202 |
| On a semilinear double fractional heat equation driven by fractional Brownian sheet |
| Dengfeng Xia,Litan Yan,Xiuwei Yin |
| Keywords:Mixed fractional heat equation, fractional Brownian sheet, H\"older regularity, Large deviation principle. |
| Abstract: |
| In this paper, we consider the stochastic heat equation of the form $$\frac{\partial u}{\partial t}=(\Delta_\alpha+\Delta_\beta)u+\frac{\partial f}{\partial x}(t,x,u)+\frac{\partial^2W}{\partial t\partial x},$$ where $1<\beta<\alpha< 2$, $W(t,x)$ is a fractional Brownian sheet, $\Delta_\theta:=-(-\Delta)^{\theta/2}$ denotes the fractional Lapalacian operator and $f:[0,T]\times \mathbb{R}\times \mathbb{R}\rightarrow\mathbb{R}$ is a nonlinear measurable function. We introduce the existence, uniqueness and H\"older regularity of the solution. As a related question, we consider also a large deviation principle associated with the above equation with a small perturbation via an equivalence relationship between Laplace principle and large deviation principle. |
PDF Download reader
|
|
|
|