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.


35R30 Inverse problems for PDEs
35K90 Abstract parabolic equations
45D05 Volterra integral equations
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