Application of Semigroup Theory to the Study of Volterra Integro-Differential Equations

• Published in: Differential equations Vol. 58; no. 4; pp. 571 - 575
• Main Authors: Vlasov, V. V., Rautian, N. A.
• Format: Journal Article
• Language: English
• Published: Moscow Pleiades Publishing 01-04-2022; Springer; Springer Nature B.V
• Subjects: Difference and Functional Equations; Differential equations; Hilbert space; Mathematics; Mathematics and Statistics; Operators (mathematics); Ordinary Differential Equations; Partial Differential Equations; Semigroups; Short Communications; Viscoelasticity; Volterra integral equations
• ISSN: 0012-2661; 1608-3083
• DOI: 10.1134/S0012266122040127

We study abstract Volterra integro-differential equations, which are operator models of problems in the theory of viscoelasticity. The class of equations under consideration also includes the Gurtin–Pipkin integro-differential equations, which describe the heat propagation process in media with memory. We present results on the existence of a strongly continuous contraction semigroup generated by a Volterra integro-differential equation with operator coefficients in a Hilbert space, as well as results on the properties of the generator of this semigroup.