Journal of Inverse and Ill-posed Problems
Editor-in-Chief: Kabanikhin, Sergey I.
6 Issues per year
IMPACT FACTOR 2016: 0.783
5-year IMPACT FACTOR: 0.792
CiteScore 2016: 0.80
SCImago Journal Rank (SJR) 2016: 0.589
Source Normalized Impact per Paper (SNIP) 2016: 1.125
Mathematical Citation Quotient (MCQ) 2015: 0.43
A degenerate parabolic identification problem: the Hilbertian case
We recover a non-negative time-dependent function, vanishing only at t = 0, in a linear multi-dimensional parabolic equation with a non-integrable degeneration concentrated at t = 0. First we prove a global in time existence and uniqueness result for the direct problem in a general Hilbert space, via Fourier representation of the solution to the direct problem. Then we show a similar result, but local in time only, for the identification problem. Finally, we apply such a result to our specific linear parabolic equation related to a smooth bounded domain in ℝd, d = 1, 2, 3.
Key words.: First-order singular in time differential equations in Hilbert space; global well-posedness of the direct problem; identifying a scalar time dependent coefficient in front of the space operator; a local in time well-posedness result for the identification problem; applications to degenerate in time differential parabolic equations
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