Period Estimates for Autonomous Evolution Equations with Lipschitz Nonlinearities

TL;DR

This paper develops a general method to estimate the minimal period of solutions in autonomous strongly damped hyperbolic and parabolic equations, extending previous results from ODEs and PDEs.

Contribution

It introduces a unified approach for period estimates applicable to both hyperbolic and parabolic problems, including beam equations.

Findings

Derived a minimal period estimate for hyperbolic problems

Extended classical results to damped hyperbolic and parabolic equations

Provided an example application to beam equations

Abstract

We derive an estimate for the minimal period of autonomous strongly damped hyperbolic problems. Our result corresponds to the works by Yorke, Busenberg et al. for ordinary differential equations as well as Robinson and Vidal-Lopez for parabolic problems. A general approach is developed for treating both hyperbolic and parabolic problems. An example of application to a class of beam equations is provided.