Advances in Differential Equations

Asymptotic expansion of solutions to an inverse problem of parabolic type

Davide Guidetti

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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.

Article information

Adv. Differential Equations, Volume 13, Number 5-6 (2008), 399-426.

First available in Project Euclid: 18 December 2012

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35R30: Inverse problems
Secondary: 35C20: Asymptotic expansions 35K90: Abstract parabolic equations


Guidetti, Davide. Asymptotic expansion of solutions to an inverse problem of parabolic type. Adv. Differential Equations 13 (2008), no. 5-6, 399--426.

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