Scientific seminar “General results on the uniqueness of solutions in linear inverse problems for differential equations in Banach spaces”
23 March at 12:00 MSK
Topic: General results on the uniqueness of solutions in linear inverse problems for differential equations in Banach spaces.
We consider an abstract differential equation of arbitrary order n in a Banach space. We assume that the equation contains an unknown element in the form of an inhomogeneous term. To find the element, in addition to the traditional Cauchy conditions, we set an additional condition at some final moment of time. In the talk, we present a general criterion for the uniqueness of solution, which is valid for similar inverse problems without any restrictions on the type of differential equation. The result is expressed in spectral terms and is closely related to the theory of the distribution of zeros of entire functions of the Mittag-Leffler type. The main working tool in the proof of the uniqueness criterion is the theory of generalized hyperbolic functions (or the so-called generalized exponentials) adapted for solving higher-order differential equations.
D. Sc., Professor Tikhonov Ivan V., Almohamed Muataz, Lomonosov Moscow State University, Moscow State Pedagogical University (Moscow).