### Asymptotic expansion of solutions to an inverse problem of parabolic type

Davide Guidetti

#### 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.

#### Article information

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

Dates
First available in Project Euclid: 18 December 2012

Mathematical Reviews number (MathSciNet)
MR2482393

Zentralblatt MATH identifier
1171.34039

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

#### Citation

Guidetti, Davide. Asymptotic expansion of solutions to an inverse problem of parabolic type. Adv. Differential Equations 13 (2008), no. 5-6, 399--426.https://projecteuclid.org/euclid.ade/1355867340