Advances in Differential Equations
- Adv. Differential Equations
- Volume 13, Number 5-6 (2008), 399-426.
Asymptotic expansion of solutions to an inverse problem of parabolic type
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.
Adv. Differential Equations, Volume 13, Number 5-6 (2008), 399-426.
First available in Project Euclid: 18 December 2012
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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