A filter regularization for recovering wave amplitude in viscoelastic media governed by fractional diffusion-wave systems

Le résumé fourni par la source

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.

Ce résumé expose les affirmations des auteurs. BNTIC ne l’interprète pas comme une validation indépendante des résultats.