Correct solvability of hyperbolic Volterra equations with kernels depending on the parameter

TL;DR

This paper investigates the conditions under which hyperbolic Volterra equations with parameter-dependent kernels are correctly solvable, with applications to thermal, viscoelastic, and heat transfer models.

Contribution

It establishes criteria for the correct solvability of a class of hyperbolic Volterra equations with kernels depending on parameters, extending existing theory.

Findings

Derived solvability conditions for parameter-dependent kernels

Applied results to models of thermal phenomena and viscoelastic media

Provided a theoretical foundation for analyzing equations with memory effects

Abstract

We study the correct solvability of an abstract functional differential equations in Hilbert space, which includes integro-differential equations describing evolution of thermal phenomena, heat transfer in materials with memory or sound propagation in viscoelastic media.