Null controllability of damped nonlinear wave equation

TL;DR

This paper establishes null controllability results for various classes of nonlinear wave equations, including semi-linear, quasi-linear, and fully nonlinear systems, using innovative mathematical methods under specific geometric conditions.

Contribution

It introduces new iterative techniques and combines classical methods to achieve controllability results for complex nonlinear wave systems.

Findings

Null controllability for semi-linear wave equations with velocity-dependent nonlinearities.

Constructive null controllability for quasi-linear wave systems via a novel iterative method.

Control results for fully nonlinear wave systems demonstrating practical applicability.

Abstract

In this paper, we investigate the null controllability of nonlinear wave systems. Initially, we employ a combination of the Galerkin method and a fixed point theorem to establish the null controllability for semi-linear wave equations with nonlinear functions that are dependent on velocities, under the geometric control condition. Subsequently, utilizing a novel iterative method, we demonstrate the null controllability for a class of quasi-linear wave systems in a constructive manner. Lastly, we present a control result for a class of fully nonlinear wave systems, serving as an application.