scholarly journals On a semilinear mixed fractional heat equation driven by fractional Brownian sheet

2017 ◽  
Vol 2017 (1) ◽  
Author(s):  
Dengfeng Xia ◽  
Litan Yan
Keyword(s):  
Heat Equation ◽  
Brownian Sheet ◽  
Fractional Brownian Sheet ◽  
Fractional Heat Equation

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

2017 ◽  
Vol 2017 ◽  
pp. 1-9 ◽  
Author(s):  
Dengfeng Xia ◽  
Litan Yan ◽  
Weiyin Fei
Keyword(s):  
Fixed Point ◽  
Heat Equation ◽  
White Noise ◽  
Existence And Uniqueness ◽  
Fractional Laplacian ◽  
Brownian Sheet ◽  
Fractional Noise ◽  
Fractional Heat Equation ◽  
Fixed Point Principle ◽  
Uniqueness Of The Solution

We consider the stochastic heat equation of the form∂u/∂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×R→Rare measurable functions. We introduce the existence and uniqueness of the solution by the fixed point principle under some suitable assumptions.

scholarly journals Determination of source term for fractional heat equation on the sphere

2020 ◽  
Vol 24 (Suppl. 1) ◽  
pp. 361-370
Author(s):  
Nguyen Phuong ◽  
Tran Binh ◽  
Nguyen Luc ◽  
Nguyen Can
Keyword(s):  
Diffusion Equation ◽  
Heat Equation ◽  
Exact Solutions ◽  
Source Term ◽  
Fractional Diffusion ◽  
Inverse Source Problem ◽  
Fractional Heat Equation ◽  
Ill Posed ◽  
Time Fractional Diffusion Equation

In this work, we study a truncation method to solve a time fractional diffusion equation on the sphere of an inverse source problem which is ill-posed in the sense of Hadamard. Through some priori assumption, we present the error estimates between the regularized and exact solutions.

scholarly journals No local L1 solutions for semilinear fractional heat equations

2017 ◽  
Vol 20 (6) ◽  
Author(s):  
Kexue Li
Keyword(s):  
Cauchy Problem ◽  
Heat Equation ◽  
Heat Equations ◽  
Fractional Heat Equation ◽  
The Cauchy Problem

AbstractWe study the Cauchy problem for the semilinear fractional heat equation

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