Geodesic
Semigroups of operators generated by integro-differential equations with kernels representable by Stieltjes integrals
Contemporary Mathematics. Fundamental Directions, Dedicated to 70th anniversary of the President of the RUDN University V. M. Filippov, Tome 67 (2021) no. 3, pp. 507-525.

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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 the contractive $C_0$-semigroup is proved. An estimate for the exponential decay of the semigroup is obtained. 
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V. V. Vlasov; N. A. Rautian. Semigroups of operators generated by integro-differential equations with kernels representable by Stieltjes integrals. Contemporary Mathematics. Fundamental Directions, Dedicated to 70th anniversary of the President of the RUDN University V. M. Filippov, Tome 67 (2021) no. 3, pp. 507-525. http://geodesic.mathdoc.fr/item/CMFD_2021_67_3_a6/

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