In this paper we prove an existence result for strict solutions to an identification problem for a first order semilinear differential equation, in a general Banach space, subjected to an overdetermination expressed by means of a Lebesgue integral. Under the additional assumption that the $C_0$-semigroup generated by the linear part has a sufficiently fast exponential decay, we prove the uniqueness and the continuous dependence of the solution on the data.
Identification for a semilinear evolution equation in a Banach space / A. Lorenzi, I.I. Vrabie. - In: INVERSE PROBLEMS. - ISSN 0266-5611. - 26:8(2010), pp. 085009.085009.1-085009.085009.16. [10.1088/0266-5611/26/8/085009]
Identification for a semilinear evolution equation in a Banach space
A. LorenziPrimo
;
2010
Abstract
In this paper we prove an existence result for strict solutions to an identification problem for a first order semilinear differential equation, in a general Banach space, subjected to an overdetermination expressed by means of a Lebesgue integral. Under the additional assumption that the $C_0$-semigroup generated by the linear part has a sufficiently fast exponential decay, we prove the uniqueness and the continuous dependence of the solution on the data.
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