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.
A degenerate parabolic identification problem: the Hilbertian case / A. Lorenzi. - In: JOURNAL OF INVERSE AND ILL-POSED PROBLEMS. - ISSN 0928-0219. - 16:9(2008), pp. 849-872.
A degenerate parabolic identification problem: the Hilbertian case
A. LorenziPrimo
2008
Abstract
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.Pubblicazioni consigliate
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