Inverse Problems for a Parabolic Integrodifferential Equation in a Convolutional Weak Form

Inverse Problems for a Parabolic Integrodifferential Equation in a Convolutional Weak Form

We deduce formulas for the Fréchet derivatives of cost functionals of several inverse problems for a parabolic integrodifferential equation in a weak formulation. The method consists in the application of an integrated convolutional form of the weak problem and all computations are implemented in re...

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Veröffentlicht in:Abstract and Applied Analysis 2013-01, Vol.2013 (2013), p.135-150-314
Hauptverfasser: Kasemets, Kairi, Janno, Jaan
Format: Artikel
Sprache:eng
Schlagworte:
Computation
Derivatives
Differential equations
Formulations
Functionals
Functions, Inverse
Integral equations
Inverse problems
Mathematical analysis
Mathematical research
Sobolev space
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Zusammenfassung:We deduce formulas for the Fréchet derivatives of cost functionals of several inverse problems for a parabolic integrodifferential equation in a weak formulation. The method consists in the application of an integrated convolutional form of the weak problem and all computations are implemented in regular Sobolev spaces.
ISSN:1085-3375
1687-0409
DOI:10.1155/2013/297104