Nonlocal Cauchy problems for wave equations and applications

TL;DR

This paper establishes existence, uniqueness, and estimates for solutions to nonlocal integral Cauchy problems in abstract wave equations, applicable to diverse physical systems through a flexible operator framework.

Contribution

It introduces a general approach to analyze nonlocal wave equations using abstract operators in Banach spaces, expanding the scope of solvable problems.

Findings

Proved existence and uniqueness of solutions

Derived estimates for solutions

Applicable to various physical models

Abstract

In this paper, the existence, the uniqueness and estimates of solution to the integral Cauchy problem for linear and nonlinear abstract wave equations are proved. The equation includes a linear operator A defined in a Banach space E, in which by choosing E and A we can obtain numerous classis of nonlocal initial value problems for wave equations which occur in a wide variety of physical systems.