Well-Posed Solvability and the Representation of Solutions of Integro-Differential Equations Arising in Viscoelasticity
- 1 Downloads
For abstract integro-differential equations with unbounded operator coefficients in a Hilbert space, we study the well-posed solvability of initial problems and carry out spectral analysis of the operator functions that are symbols of these equations. This allows us to represent the strong solutions of these equations as series in exponentials corresponding to points of the spectrum of operator functions. The equations under study are the abstract form of linear integro-partial differential equations arising in viscoelasticity and several other important applications.
Unable to display preview. Download preview PDF.
- 1.Il’yushin, A.A. and Pobedrya, B.E., Osnovy matematicheskoi teorii termovyazkouprugosti (Foundations of Mathematical Theory of Thermoviscoelasticity), Moscow: Nauka, 1970.Google Scholar
- 2.Rabotnov, Yu.N., Elementy nasledstvennoi mekhaniki tverdykh tel (Elements of Hereditary Mechanics of Solids), Moscow: Nauka, 1977.Google Scholar
- 3.Lykov, A.V., Problema teplo- i massoobmena (Heat and Mass Exchange Problem), Minsk: Nauka i Tekhnika, 1976.Google Scholar
- 12.Vlasov, V.V. and Rautian, N.A., Properties of solutions of integro-differential equations arising in heat and mass transfer theory, Trans. Mosc. Math. Soc., 2014, pp. 185–204.Google Scholar
- 13.Vlasov, V.V. and Rautian, N.A., Spektral’nyi analiz funktsional’no-differentsialnykh uravnenii (Spectral Analysis of Functional-Differential Equations), Moscow: MAKS Press, 2016.Google Scholar