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

Autor:	Vlasov, V. V., Rautian, N. A.
Předmět:	STIELTJES integrals INTEGRAL equations DIFFERENTIAL equations INTEGRO-differential equations VOLTERRA equations OPERATOR equations
Zdroj:	Journal of Mathematical Sciences; Jan2024, Vol. 278 Issue 2, p287-305, 19p
Abstrakt:	Abstract 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 C0-semigroup is proved. An estimate for the exponential decay of the semigroup is obtained. [ABSTRACT FROM AUTHOR]
Databáze:	Complementary Index
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