Backward problems in time for fractional diffusion-wave equation

Abstract

Abstract In this article, for a time-fractional diffusion-wave equation ∂ t α u ( x , t ) = − A u ( x , t ) , 0 < t < T with fractional order α ∈ (1, 2), we consider the backward problem in time: determine u(⋅, t), 0 < t < T by u(⋅, T) and ∂ t u(⋅, T). We prove that there exists a countably infinite set Λ ⊂ (0, ∞) with a unique accumulation point 0 such that the backward problem is well-posed for T ∉ Λ.