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A degenerate parabolic identification problem: the Hilbertian case
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A. Lorenzi
Published/Copyright:
December 8, 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.
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
Received: 2008-08-28
Published Online: 2008-12-08
Published in Print: 2008-December
© de Gruyter 2008
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Keywords for this article
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
Articles in the same Issue
- On wave fields generated by the sources disposed in the infinity
- Inverse problem for a semilinear functional-differential wave equation
- A degenerate parabolic identification problem: the Hilbertian case
- Coarse-to-fine reconstruction in linear inverse problems with application to limited-angle computerized tomography
- Inverse problems for vibrating systems of first order
