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
Davide Guidetti. "Asymptotic expansion of solutions to an inverse problem of parabolic type." Adv. Differential Equations 13 (5-6) 399 - 426, 2008. https://doi.org/10.57262/ade/1355867340
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