Backward problems in time for fractional diffusion-wave equation

In this article, for a time-fractional diffusion-wave equation , 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. © 2020 IOP Publishing Ltd.

Authors
Floridia G. 1, 5 , Yamamoto M. 2, 3, 4
Journal
Inverse Problems
Publisher
Institute of Physics Publishing
Issue number
12
Language
English
State
Published
Link
External link
DOI
10.1088/1361-6420/ABBC5E
Number
125016
Volume
36
Year
2020
Organizations
  • 1 Department PAU, Universita Mediterranea di Reggio Calabria, Via dell'Universita 25, Reggio Calabria, 89124, Italy
  • 2 Graduate School of Mathematical Sciences, The University of Tokyo, Komaba, Meguro, Tokyo, 153-8914, Japan
  • 3 Honorary Member of Academy of Romanian Scientists, Splaiul Independentei Street, no 54, Bucharest, 050094, Romania
  • 4 Peoples' Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya St, Moscow, 117198, Russian Federation
  • 5 INdAM Unit, University of Catania, Italy
Keywords
Computer applications; Signal processing; Accumulation points; Backward problems; Fractional diffusion; Fractional order; Time-fractional diffusion; Wave equations
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