Enviar artigo por via de e-mail STUDY OF VOLTERRA INTEGRO-DIFFERENTIAL EQUATIONS BY METHODS OF SEMIGROUP THEORY
- Autores: Rautian N.A.1
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Afiliações:
- Lomonosov Moscow State University, Moscow Center for Fundamental and Applied Mathematics
- Edição: Volume 513, Nº 1 (2023)
- Páginas: 88-92
- Seção: MATHEMATICS
- URL: https://rjeid.com/2686-9543/article/view/647912
- DOI: https://doi.org/10.31857/S2686954323600283
- EDN: https://elibrary.ru/XRBNBC
- ID: 647912
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Resumo
The abstract Volterra integro-differential equations are investigated, which are operator models of problems of viscoelasticity theory. The class of equations under consideration also includes the Gurtin-Pipkin integro-differential equations describing the process of heat propagation in media with memory. The sums of decreasing exponents or sums of Rabotnov functions with positive coefficients can be considered in particular as the kernels of integral operators, which are widely used in the theory of viscoelasticity and heat propagation theory.
Sobre autores
N. Rautian
Lomonosov Moscow State University, Moscow Center for Fundamental and Applied Mathematics
Autor responsável pela correspondência
Email: nadezhda.rautian@math.msu.ru
Russia, Moscow
Bibliografia
- Kopachevsky N.D., Krein S.G. Operator Approach to Linear Problems of Hydrodynamics. Vol. 2: Nonself-adjoint Problems for Viscous Fluids // Operator Theory: Advances and Applications (Birkhauser Verlag, Basel/Switzerland). 2003. V. 146. 444 p.
- Amendola G., Fabrizio M., Golden J.M. Thermodynamics of Materials with memory.Theory and applications. New-York–Dordrecht–Heidelberg–London, Springer, 2012. 576 p.
- Локшин А.А., Суворова Ю.В. Математическая теория распространения волн в средах с памятью. М.: Изд-во МГУ, 1982. 152 с.
- Gurtin M.E., Pipkin A.C. General theory of heat conduction with finite wave speed // Arch. Rat. Mech. Anal. 1968. V. 31. P. 113–126.
- Санчес-Паленсия Э. Неоднородные среды и теория колебаний. М.: Мир, 1984.
- Работнов Ю.Н. Элементы наследственной механики твердых тел. М.: “Наука”, 1977. 384 с.
- Shamaev A.S., Shumilova V.V. Spectrum of one-dimensional eigenoscillations of a medium consisting of viscoelastic material with memory and incompressible viscous fluid // Journal of Mathematical Sciences. 2021. V. 257. № 5. P. 732–742.
- Vlasov V.V., Rautian N.A. Correct solvability and representation of solutions of Volterra integrodifferential equations with fractional exponential kernels // Doklady Mathematics. 2019. V. 100. № 2. P. 467–471.
- Rautian N.A. Semigroups Generated by Volterra Integro-Differential Equations // Differential Equations. 2020. V. 56. № 9. P. 1193–1211.
- Rautian N.A. Exponential stability of semigroups generated by volterra integro-differential equations // Ufa Mathematical Journal. 2021. V. 13. № 4. P. 65–81.
- Skubachevskii A.L. Boundary-value problems for elliptic functional-differential equations and their applications // Russian Mathematical Surveys. 2016. V. 71. № 5. P. 801–906.
- Kato T. Perturbation theory for linear operators. Springer, 1966.
- Крейн С.Г. Линейные дифференциальные уравнения в банаховых пространствах. М.: “Наука”, 1967. 464 с.
- Engel K.J., Nagel R. One-Parameter Semigroups for Linear Evolution Equations. Springer-Verlag, New York, 2000. 586 p.
- Колмогоров А.Н., Фомин С.В. Элементы теории функций и функционального анализа. М. “Наука”, 1989.
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