Speciality:
01.01.02 (Differential equations, dynamical systems, and optimal control)
Birth date:
19.02.1961
E-mail: Keywords: differential equations in Banach spaces; generalized functions; integral equations of the 1-ht kind; theory of semigroups of operators.
Subject:
In several papers the problem of generalized solutions construction of degenerated differential and integral equations in Banach spaces was investigated. In the last of papers (SMJ, 2000, v. 41, no. 5) this problem was solved by fundamental operator construction for some classes of differential, integral and integro-differential operators. Some papers concern the development of analytical theory of the systems of Volterra integral equations, used in the construction of logariphm-power solutions of these systems. These ideas allow to construct the similar solutions for the integral equations with the singularities. For the integral Volterra equation of the first kind the problem of correct statement and construction of generalized solutions in the Schwarz distribution class with the left bounded carrier was solved.
Main publications:
Falaleev M. V. Asymptotic expansions of continuous solutions of system of Volterra integral equations of the first kind // International symposium on computerized tomography. Novosibirsk, Russia, August 10–14, 1993. Amsterdam, Nord-Holl, 1994, p. 155–157.
