Speciality:
01.01.02 (Differential equations, dynamical systems, and optimal control)
Birth date:
1.03.1972
E-mail: Website: https://www.csu.ru/main.asp?method=GetPage&p=497&redir=595 Keywords: operator semigroups,
Sobolev type equations,
initial boundary value problem,
inverse problem,
optimal control problem distributed system,
degenerate semigroup of operators,
unique solvability.
UDC: 517.955.4, 517.983.5, 517.977, 517.9, 517.983, 517.97, 517.977.1 MSC: 47D03, 47D06, 34G10, 34G25, 35A25, 35G10
Subject:
Resolving semigroups from various classes of smoothness of the Sobolev type equations $L\dot u=Mu$ in locally convex space are investigated. They have nontrivial kernels therefore their kernels and images are researched. It is shown that the phase space of the linear Sobolev type equation coincide with the image of its semigroup. The generation theorems are generalized on the cases of degenerate semigroups of operators. The abstract results are applied to research of initial boundary value problems for nonclassical partial derivative equations.
Perurbed Sobolev type equations, inverse and optimal control problems for distributed systems unsolved with respect to the time derivative are considered.
Main publications:
Fedorov V. E., “Degenerate strongly continuous semigroups of operators”, St. Petersburg Math. J., 12:3 (2001), 471–489
Fedorov V. E., “Weak solutions of linear equations of Sobolev type and semigroups of operators”, Izv. Math., 67:4 (2003), 797–813
Sviridyuk G. A., Fedorov V. E., Linear Sobolev Type Equations and Degenerate Semigroups of Operators, Inverse and Ill-Posed Problems, VSP, Utrecht; Boston, 2003
Fedorov V. E., “Holomorphic solution semigroups for Sobolev-type equations in locally convex spaces”, Sb. Math., 195:8 (2004), 1205–1234
Fedorov V. E., “A generalization of the Hille-Yosida theorem to the case of degenerate semigroups in locally convex spaces”, Sib. Math. J., 46:2 (2005), 333–350
