Inverse Problem in the Space of Generalized Functions

For a linear nonhomogeneous diffusion equation with fractional derivative of order β 2 (0 , 2) with respect to time, we establish the unique solvability of the inverse problem of determination of a pair of functions: the generalized solution u (classical as a function of time) of the first boundary-...

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Bibliographic Details
Published in:Ukrainian mathematical journal 2016-07, Vol.68 (2), p.269-282
Main Authors: Lopushans’kyi, A., Lopushans’ka, H., Rapita, V.
Format: Article
Language:English
Subjects:
Algebra
Analysis
Applications of Mathematics
Boundary value problems
Continuity (mathematics)
Geometry
Inverse problems
Mathematics
Mathematics and Statistics
Statistics
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Summary:For a linear nonhomogeneous diffusion equation with fractional derivative of order β 2 (0 , 2) with respect to time, we establish the unique solvability of the inverse problem of determination of a pair of functions: the generalized solution u (classical as a function of time) of the first boundary-value problem for the indicated equation with given generalized functions on the right-hand sides and the unknown (depending on time) continuous coefficient of the minor term of the equation under the overdetermination condition u ⋅ t , φ 0 ⋅ = F t , t ∈ 0 T . Here, F is a given continuous function and ( u ( ·, t ) , φ 0 ( · )) is the value of the unknown generalized function u on a given test function φ 0 for any t 2 [0 ,T ] .
ISSN:0041-5995
1573-9376
DOI:10.1007/s11253-016-1223-4