A filter regularization for recovering wave amplitude in viscoelastic media governed by fractional diffusion-wave systems
Year: 2026
Type: article
Abstract: In this paper, we consider a final value problem for the following time-fractional diffusion system: { D t α u + 𝒜 u = F ( u , v ) , D t α v + ℬ v = G ( u , v ) , \left\{\begin{aligned} \displaystyle{}D_{t}^{\alpha}u+\mathcal{A}u&% \displaystyle=F(u,v),\\ \displaystyle D_{t}^{\alpha}v+\mathcal{B}v&\displaystyle=G(u,v),\end{aligned}\right. where 𝒜 {\mathcal{A}} and ℬ {\mathcal{B}} are symmetric uniformly elliptic operators defined on a bounded domain Ω in ℝ d {\mathbb{R}^{d}} with sufficiently smooth boundary and D t α {D_{t}^{\alpha}} refers to the Caputo fractional derivative of order 1 < α < 2 {1<\alpha<2} . Under suitable assumptions, we establish the existence and uniqueness of the solution to the problem and prove that the problem is ill-posed in the sense of Hadamard. A filter regularization method is proposed to approximate the solution and estimate the error between the regularized solution and the exact solution.
Institution: Saigon University
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $2,712
OpenAlex ID: W7140700730