Smoothing property of solutions to nonlocal hyperbolic problems

TL;DR

This paper investigates nonlocal hyperbolic systems with integral boundary conditions, demonstrating that their solutions become continuous over time despite initial irregularities.

Contribution

It establishes a general regularity result showing that $L^2$-generalized solutions to these problems become eventually continuous, advancing understanding of nonlocal hyperbolic systems.

Findings

Solutions become continuous over time

General regularity result for nonlocal hyperbolic systems

Enhances understanding of solution behavior in integro-differential problems

Abstract

We consider nonlocal initial boundary value problems with integral boundary conditions for integro-differential first order hyperbolic systems. We prove a general regularity result stating that the $L^2$-generalized solutions become eventually continuous.