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Well-Posed Solvability and the Representation of Solutions of Integro-Differential Equations Arising in Viscoelasticity

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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… Click to show full abstract

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.

Keywords: integro differential; well posed; arising viscoelasticity; differential equations; equations arising; posed solvability

Journal Title: Differential Equations
Year Published: 2019

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