Multipoint Cauchy problem for nonlinear wave equations in vector-valued spaces

TL;DR

This paper investigates regularity and Strichartz estimates for solutions to multipoint Cauchy problems of linear and nonlinear wave equations in vector-valued spaces, encompassing diverse physical models.

Contribution

It introduces new regularity and Strichartz estimates for multipoint Cauchy problems in abstract wave equations within vector-valued function spaces.

Findings

Established regularity properties of solutions.

Derived Strichartz type estimates for the solutions.

Applicable to various physical systems through operator choices.

Abstract

In this paper, regularity properties, Strichartz type estimates to solutions of multipo{\i}nt Cauchy problem for linear and nonlinear abstract wave equations in vector-valued function spaces are obtained. The equation includes a linear operator A defined in a Hilbert space H, in which by choosing H and A we can obtain numerous classis of nonlocal initial value problems for wave equations which occur in a wide variety of physical systems.