Abstract Volterra integral equations of wave type with almost sectorial operators
Analysis of PDEs
2025-09-08 v1 Functional Analysis
Abstract
We study classical solutions (existence, uniqueness, and explicit solution operator) for homogeneous, linear, and semilinear abstract Volterra integral equations of wave type with almost sectorial operators. We use a functional calculus for the latter type of operators to construct a general class of bounded linear operators that in particular contains the propagators (solution operators) of the considered equations. Some properties of this family of operators are also given.
Keywords
Cite
@article{arxiv.2509.05229,
title = {Abstract Volterra integral equations of wave type with almost sectorial operators},
author = {Joel E. Restrepo},
journal= {arXiv preprint arXiv:2509.05229},
year = {2025}
}