ON A SEMILINEAR DOUBLE FRACTIONAL HEAT EQUATION DRIVEN BY FRACTIONAL BROWNIAN SHEET

Dengfeng Xia; Litan Yan; Xiuwei Yin

doi:10.11948/2018.202

2018 Volume 8 Issue 1

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Dengfeng Xia, Litan Yan, Xiuwei Yin. ON A SEMILINEAR DOUBLE FRACTIONAL HEAT EQUATION DRIVEN BY FRACTIONAL BROWNIAN SHEET[J]. Journal of Applied Analysis & Computation, 2018, 8(1): 202-228. doi: 10.11948/2018.202

Citation:

Dengfeng Xia, Litan Yan, Xiuwei Yin. ON A SEMILINEAR DOUBLE FRACTIONAL HEAT EQUATION DRIVEN BY FRACTIONAL BROWNIAN SHEET[J]. Journal of Applied Analysis & Computation, 2018, 8(1): 202-228. doi: 10.11948/2018.202

ON A SEMILINEAR DOUBLE FRACTIONAL HEAT EQUATION DRIVEN BY FRACTIONAL BROWNIAN SHEET

1 School of Mathematics and Physics, Anhui Polytechnic University, Wuhu, Anhui 241000, China;
2 Department of Mathematics, College of Science, Donghua University, 2999 North Renmin Rd., Songjiang, Shanghai 201620, China

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Abstract

Abstract

In this paper, we consider the stochastic heat equation of the form ∂u/∂t=(∆_α + ∆_β)u + ∂f/∂x (t, x, u) + ∂²W/∂t∂x, where 1 < β < α < 2, W(t, x) is a fractional Brownian sheet, ∆_θ:=-(-∆)^θ/2 denotes the fractional Lapalacian operator and f:[0, T]×R×R → R is a nonlinear measurable function. We introduce the existence, uniqueness and Hölder 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.
- Mixed fractional heat equation /
- fractional Brownian sheet /
- Hölder regularity /
- Large deviation principle
MSC: 60H15;60F10;60G22

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References

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