Qualitative properties of the fourth-order hyperbolic equations

TL;DR

This paper studies the qualitative behavior of weak solutions to fourth-order hyperbolic equations with constant coefficients, focusing on maximum principles, solvability, and uniqueness in convex domains with low regularity data.

Contribution

It extends classical results to fourth-order hyperbolic equations with minimal regularity assumptions on initial data, establishing maximum principles and uniqueness.

Findings

Proved maximum principle for weak solutions.

Established solvability of boundary value problems.

Demonstrated uniqueness under weak regularity conditions.

Abstract

We investigate the qualitative properties of the weak solutions to the boundary value problems for the hyperbolic fourth-order linear equations with constant coefficients in the plane bounded domain convex with respect to characteristics. The main question is to prove the analogue of maximum principle, solvability and uniqueness results for the weak solutions of initial and boundary value problems in the case of weak regularities of initial data from $L^2.$