Scientific seminar “Study of Volterra integro-differential equations in Hilbert space and their applications”
11 April at 12.00 (Moscow time)
Speaker: Rautian Nadezhda Alexandrovna, Doctor of Physical and Mathematical Sciences, Associate Professor of the Department of Mathematical Analysis, Faculty of Mechanics and Mathematics, Lomonosov Moscow State University.
Topic: Study of Volterra integro-differential equations in Hilbert space and their applications.
The research is aimed at studying the asymptotic and qualitative properties of solutions of integro-differential equations and equations with unbounded operator coefficients in a Hilbert space. The main part of the equations under consideration is an abstract hyperbolic equation perturbed by terms containing Volterra integral operators. These integro-differential equations are generalized linear models of viscoelasticity, diffusion and heat conduction in media with memory (the Gurtin-Pipkin equation) and have a number of other important applications.
For a wide class of kernels of integral operators, results are established on the existence and uniqueness of classical solutions of these equations, obtained on the basis of an approach related to the application of the theory of semigroups of operators.
The spectral analysis of generators of semigroups of operators generated by the indicated integro-differential equations is carried out. Based on the results obtained earlier, a connection is established between the spectra of operator-functions, which are symbols of the indicated integro-differential equations, and the spectra of generators of semigroups of operators. Based on the spectral analysis of the generators of semigroups of operators and the corresponding operator functions, representations of solutions of the considered integro-differential equations are obtained.