# Bounded Solutions to Boundary Value Hyperbolic Problems

## TL;DR

This paper studies conditions for existence and uniqueness of bounded solutions to first-order hyperbolic boundary value problems in a strip, focusing on zero-order coefficients and dissipativity conditions.

## Contribution

It provides new criteria for bounded solutions in hyperbolic systems, emphasizing the role of zero-order coefficients and boundary data.

## Key findings

- Established conditions for existence and uniqueness of solutions.
- Identified the importance of zero-order coefficient behavior at infinity.
- Formulated dissipativity conditions related to boundary data.

## Abstract

We investigate linear boundary value problems for first-order one-dimensional hyperbolic systems in a strip. We establish conditions for existence and uniqueness of bounded continuous solutions. For that we suppose that the non-diagonal part of the zero-order coefficients vanish at infinity. Moreover, we establish a dissipativity condition in terms of the boundary data and the diagonal part of the zero-order coefficients.