Semigroups of Operators Generated by Integro-Differential Equations with Kernels Representable by Stieltjes Integrals

• Published in: Journal of mathematical sciences (New York, N.Y.) Vol. 278; no. 2; pp. 287 - 305
• Main Authors: Vlasov, V. V., Rautian, N. A.
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 2024; Springer Nature B.V
• Subjects: Cauchy problems; Differential equations; Function space; Hilbert space; Integrals; Linear evolution equations; Mathematics; Mathematics and Statistics; Operators (mathematics); Semigroups; Volterra integral equations; Stieltjes integral; semigroup; contractive; abstract Volterra integro-differential equation; one-parameter semigroup
• ISSN: 1072-3374; 1573-8795
• DOI: 10.1007/s10958-024-06920-9

Volterra integro-differential equations with kernels of integral operators representable by Stieltjes integrals are investigated. The presented results are based on the approach related to the study of one-parameter semigroups for linear evolution equations. We present the method of reduction of the original initial-value problem for a model integro-differential equation with operator coefficients in a Hilbert space to the Cauchy problem for a first-order differential equation in an extended function space. The existence of a contractive
C
0
-semigroup is proved. An estimate for the exponential decay of the semigroup is obtained.