An inverse random source problem for the time-space fractional diffusion equation driven by fractional Brownian motion

06/02/2021 ∙ by Daxin Nie, et al. ∙ 0

We study the inverse random source problem for the time-space fractional diffusion equation driven by fractional Brownian motion with Hurst index H∈(0,1). With the aid of a novel estimate, by using the operator approach we propose regularity analyses for the direct problem. Then we provide a reconstruction scheme for the source terms f and g up to the sign. Next, combining the properties of Mittag-Leffler function, the complete uniqueness and instability analyses are provided. It's worth mentioning that all the analyses are unified for H∈(0,1).

READ FULL TEXT
POST COMMENT

Comments

There are no comments yet.

Authors

page 1

page 2

page 3

page 4

This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.