N. D. Kopachevsky, E. V. Syomkina, “Linear Volterra integro-differential second-order equations unresolved with respect to the highest derivative”, Eurasian Math. J., 2013, Volume 4, Number 4,Pages <nobr>64

This article is cited in 3 papers

Linear Volterra integro-differential second-order equations unresolved with respect to the highest derivative

N. D. Kopachevsky, E. V. Syomkina

Department of Mathematics and Informatics, Taurida National V. Vernadsky University, Academician Vernadsky Ave. 4, 95007 Simferopol, Ukraine

Abstract: We consider the Cauchy problem for Volterra integro-differential secondorder linear equations which describe an evolution of dynamical systems with infinite numbers of degrees of freedom taking into account relaxation effects. Existence theorems for strong solutions for three classes of complete integro-differential second-order equations are obtained.

Keywords and phrases: Volterra integro-differential equation, $C_0$-semigroup, self-adjoint operator.

MSC: 39B42, 39B99

Received: 25.10.2013

Language: English