Uniqueness of solution with zero boundary condition for time-fractional wave equations

We consider a solution u to an initial boundary value problem in a bounded domain Ω over a time interval (0,T) for a time-fractional wave equation where the order of time derivative is between 1 and 2. We prove that if u|ω×(0,T)=0 for arbitrarily chosen subdomain ω⊂Ω, then u=0 in Ω×(0,T).

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Bibliographic Details
Published in:Applied mathematics letters 2024-02, Vol.148, p.108862, Article 108862
Main Authors: Loreti, Paola, Sforza, Daniela, Yamamoto, M.
Format: Article
Language:English
Subjects:
Caputo derivative
Initial value
Inverse problem
Time-fractional wave equation
Uniqueness
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Summary:We consider a solution u to an initial boundary value problem in a bounded domain Ω over a time interval (0,T) for a time-fractional wave equation where the order of time derivative is between 1 and 2. We prove that if u|ω×(0,T)=0 for arbitrarily chosen subdomain ω⊂Ω, then u=0 in Ω×(0,T).
ISSN:0893-9659
1873-5452
DOI:10.1016/j.aml.2023.108862