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Issue: Vol. 3 No. 101 (2025)
Section: Articles
Date Published: 27/03/2026
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Le, M. T., & Nguyen, M. H. (2026). Regularization of a Final Value Problem for a System of Nonlinear Time- Fractional Diffusion-Wave Equations. Scientific Journal of Saigon University, 3(101), 102-121. https://sj.sgu.edu.vn/index.php/sjsgu/article/view/415

Regularization of a Final Value Problem for a System of Nonlinear Time- Fractional Diffusion-Wave Equations

Minh Triet Le1, , Minh Hoang Nguyen2
1 Saigon University
2 Nghiên cứu sinh, Trường Đại học Sài Gòn

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Abstract

In this paper, we consider a final value problem for the following time-fractional diffusion-wave system 


where  denotes the Laplace operator defined on a bounded domain Ω in ℝd with sufficiently smooth boundary and  refers to the Caputo fractional derivative of order 1 < α < 2. Under suitable assumptions on the nonlinear terms and the solution, we prove the existence and uniqueness of a solution to the problem. We also show that the final value problem is ill-posed in the sense of Hadamard. Finally, we propose a truncation regularization method to approximate the solution and derive an error estimate between the regularized solution and the exact solution, with a convergence rate of order √ε.

Keywords

Time-fractional diffusion equation, nonlinear source term, ill-posedness, final value problem, fractional diffusion system, backward problem, regularization.

Article Details

References

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