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

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{CMFD_2021_67_3_a6,
     author = {V. V. Vlasov and N. A. Rautian},
     title = {Semigroups of operators generated by integro-differential equations with kernels representable by {Stieltjes} integrals},
     journal = {Contemporary Mathematics. Fundamental Directions},
     pages = {507--525},
     publisher = {mathdoc},
     volume = {67},
     number = {3},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CMFD_2021_67_3_a6/}
}
TY  - JOUR
AU  - V. V. Vlasov
AU  - N. A. Rautian
TI  - Semigroups of operators generated by integro-differential equations with kernels representable by Stieltjes integrals
JO  - Contemporary Mathematics. Fundamental Directions
PY  - 2021
SP  - 507
EP  - 525
VL  - 67
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CMFD_2021_67_3_a6/
LA  - ru
ID  - CMFD_2021_67_3_a6
ER  - 
%0 Journal Article
%A V. V. Vlasov
%A N. A. Rautian
%T Semigroups of operators generated by integro-differential equations with kernels representable by Stieltjes integrals
%J Contemporary Mathematics. Fundamental Directions
%D 2021
%P 507-525
%V 67
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CMFD_2021_67_3_a6/
%G ru
%F CMFD_2021_67_3_a6
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/