SIMULTANEOUS DETERMINATION OF INITIAL VALUE AND SOURCE TERM FOR TIME-FRACTIONAL WAVE-DIFFUSION EQUATIONS
Paola Loreti, Daniela Sforza, Masahiro Yamamoto
article (Uluslararası, Hakemli) | Yazar(lar): Paola Loreti, Daniela Sforza, Masahiro Yamamoto | Yıl: 2026 | Dergi/Kurum: INVERSE PROBLEMS AND IMAGING | İndeks: WOS.SCI | DOI: 10.3934/ipi.2025025 | Anahtar Kelimeler: Time-fractional diffusion-wave equations, inverse source problem, initial value, uniqueness — Özet: We c
We consider initial boundary value problems for time fractional diffusion-wave equations: d(t)(alpha) u(x, t) = -Au(x, t) + mu(t)f (x) in a bounded domain Omega subset of R-d, where alpha is an element of (0, 1) boolean OR (1, 2), mu(t)f(x) describes a source, and-A is a symmetric elliptic operator: -Av(x) = Sigma(d)(i,j=1) partial derivative(i)(a(ij)(x)partial derivative(j)v(x)) + c(x)v(x) for x is an element of Omega. We assume that there exists T > 0 such that mu(t) = 0 for t > T. For T-2 > T-1 > T, we prove the uniqueness in simultaneously determining f in Omega, mu in (0, T), and initial values of u by data u|(omega x(T1,T2)), provided that the order alpha does not belong to an at most countably infinite set in (0,1) boolean OR (1,2) which is characterized by mu. The proof is based on the asymptotic expansion of the solution u by means of the Mittag-Leffler functions.