Periodic solutions for nonlinear hyperbolic evolution systems
Piotr Kokocki, Aleksander \'Cwiszewski
TL;DR
This paper establishes an averaging principle for nonlinear hyperbolic evolution systems, proving the existence of periodic solutions and applying the results to damped hyperbolic PDEs.
Contribution
It introduces a new averaging principle for nonlinear hyperbolic evolution equations using topological degree theory.
Findings
Proves existence of periodic solutions for nonlinear hyperbolic systems.
Develops an averaging method based on translation along trajectories.
Applies abstract results to specific damped hyperbolic PDEs.
Abstract
We shall deal with the periodic problem for nonlinear perturbations of abstract hyperbolic evolution equations generating an evolution system of contractions. We prove an averaging principle for the translation along trajectories operator associated to the nonlinear evolution system, expressed in terms of the topological degree. The abstract results shall be applied to the damped hyperbolic partial differential equation.
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Taxonomy
TopicsStability and Controllability of Differential Equations · Nonlinear Differential Equations Analysis · Advanced Mathematical Physics Problems