The Inverse Source Problem for a Class of Stochastic Convection-Diffusion Equations

ZHAO Lizhi; FENG Xiaoli

doi:10.21656/1000-0887.420399

Volume 43 Issue 12

Dec. 2022

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ZHAO Lizhi, FENG Xiaoli. The Inverse Source Problem for a Class of Stochastic Convection-Diffusion Equations[J]. Applied Mathematics and Mechanics, 2022, 43(12): 1392-1401. doi: 10.21656/1000-0887.420399

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The Inverse Source Problem for a Class of Stochastic Convection-Diffusion Equations

doi: 10.21656/1000-0887.420399

ZHAO Lizhi,
FENG Xiaoli^,

School of Mathematics and Statistics, Xidian University, Xi’an 710126, P.R.China

Received Date: 2021-12-17
Accepted Date: 2022-02-12
Rev Recd Date: 2022-02-12

Available Online: 2022-11-07

Publish Date: 2022-12-01

Abstract

Abstract

The inverse source problem for a class of stochastic convection-diffusion equations driven by the fractional Brownian motion with the Hurst index, was considered. The direct problem is to study the solution to the stochastic convection-diffusion equation. The inverse problem is to determine the statistical properties of the source from the expectation and covariance of the final-time data. The direct problem is well-posed. The uniqueness and instability of the inverse source problem was proved. Some numerical simulation examples verify the theoretical analysis.
- stochastic convection-diffusion equation,
- inverse source problem,
- fractional Brownian motion,
- uniquness,
- ill-posedness

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References

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