×

An inverse problem for an abstract evolution equation. (English) Zbl 1020.35120

Summary: The inverse problem of finding the coefficient \(\gamma\) in the equation \(\dot u= A(t)u+ \gamma(t)u+ f(t)\) from the extra data of the form \(\phi(t)= \langle u(t),w\rangle\) is studied. The problem is reduced to a Volterra equation of the second kind. Applications are given to parabolic equations with second-order differential operators.

MSC:

35R30 Inverse problems for PDEs
35K90 Abstract parabolic equations
45D05 Volterra integral equations
PDF BibTeX XML Cite
Full Text: DOI arXiv Link

References:

[1] Daletsky Yu.L, Mathematics and its Application 76 (1991)
[2] Kamynin, V. and Saroldi, M. ”On an Inverse Problem of Recovering a Coefficient in Second order parabolic Equation of Non-divergent Type”. Vol. 83, 1–14. Pubblicazioni dell’instituto di analisi globale applicationi.
[3] Pazy A., Semigroups of Linear Operators and Applications to Partial Differential Equations (1983) · Zbl 0516.47023
[4] Ladyhenskaya O., Lineur and Quasi-linear Equations of Parabolic Type (1968)
[5] Lorenzi A., Nonlinear Functional Analysis and Applications 6 pp 107– (2001)
[6] Prilepko A., Diff. Eq 23 pp 136– (1987)
[7] Protter M., Maximum Principles in Differential Equations (1967) · Zbl 0153.13602
[8] Ramm A.G., Operator Theory and its Applications, Amer. Math. Soc 25 pp 15– (2000)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.