The Backward Problem for the Nonlinear Space-Fractional Diffusion Equation with Gaussian White Noise
2
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
In this paper, we consider the problem of reconstructing the heat distribution for a nonlinear space-fractional diffusion equation from the final data with Gaussian white noise. As is commonly acknowledged, the problem is severely ill-posed according to Hadamard’s definition. Consequently, we propose the Fourier truncation method to regularize the problem. With different assumptions on the exact solution, we obtain an estimation of the expectation of the error between the regularized solution and the exact solution. Finally, we provide an example to illustrate our theoretical results.
Abstract
In this paper, we consider the problem of reconstructing the heat distribution for a nonlinear space-fractional diffusion equation from the final data with Gaussian white noise. As is commonly acknowledged, the problem is severely ill-posed according to Hadamard’s definition. Consequently, we propose the Fourier truncation method to regularize the problem. With different assumptions on the exact solution, we obtain an estimation of the expectation of the error between the regularized solution and the exact solution. Finally, we provide an example to illustrate our theoretical results.