Mixed Fractional Heat Equation Driven by Fractional Brownian Sheet and Lévy Process

Author:

Xia Dengfeng12ORCID,Yan Litan13ORCID,Fei Weiyin2

Affiliation:

1. College of Information Science and Technology, Donghua University, 2999 North Renmin Rd., Songjiang, Shanghai 201620, China

2. School of Mathematics and Physics, Anhui Polytechnic University, Wuhu, Anhui 241000, China

3. Department of Mathematics, College of Science, Donghua University, 2999 North Renmin Rd., Songjiang, Shanghai 201620, China

Abstract

We consider the stochastic heat equation of the formu/t=(Δ+Δα)u+(f/x)(t,x,u)+σ(t,x,u)L˙+W˙H,whereW˙His the fractional noise,L˙is a (pure jump) Lévy space-time white noise,Δis Laplacian, andΔα=-(-Δ)α/2is the fractional Laplacian generator onR, andf,σ:[0,T]×R×RRare measurable functions. We introduce the existence and uniqueness of the solution by the fixed point principle under some suitable assumptions.

Funder

National Natural Science Foundation of China

Publisher

Hindawi Limited

Subject

General Engineering,General Mathematics

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