# Regularity of complexified hyperbolic equations with integral conditions

## TL;DR

This paper studies hyperbolic wave equations with non-local integral conditions, demonstrating that solutions can be regularized using complex exponential weights and establishing their existence, uniqueness, and regularity.

## Contribution

It introduces a method to achieve regularity for complexified hyperbolic equations with integral conditions using harmonic exponential weights, extending previous results.

## Key findings

- Existence and uniqueness of solutions proven.
- Regularity of solutions established.
- Method for complexified problems with integral conditions introduced.

## Abstract

This paper considers hyperbolic wave equations with non-local in time conditions involving integrals with respect to time. It is shown that regularity of the solution can be achieved for complexified problem with integral conditions involving harmonic complex exponential weights. The paper establishes existence, uniqueness, and a regularity of the solutions.