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2008 Asymptotic expansion of solutions to an inverse problem of parabolic type
Davide Guidetti
Adv. Differential Equations 13(5-6): 399-426 (2008).

Abstract

We consider an abstract linear parabolic problem, with a scalar part $f$ of the source term which is unknown. This lack of information is compensated by the knowledge, for any time, of the value of a certain functional $\Phi$ when applied to the solution. Under suitable assumptions, we prove a result of global existence and uniqueness of the solution $(u,f)$. Moreover, if the coefficients of the system admit an asymptotic expansion, the same holds for $(u,f)$. The abstract results are applied to general parabolic mixed Cauchy-boundary value problems.

Citation

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Davide Guidetti. "Asymptotic expansion of solutions to an inverse problem of parabolic type." Adv. Differential Equations 13 (5-6) 399 - 426, 2008.

Information

Published: 2008
First available in Project Euclid: 18 December 2012

zbMATH: 1171.34039
MathSciNet: MR2482393

Subjects:
Primary: 35R30
Secondary: 35C20, 35K90

Rights: Copyright © 2008 Khayyam Publishing, Inc.

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Vol.13 • No. 5-6 • 2008
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