Publication

Boundary Stabilization of Focusing NLKG near Unstable Equilibria: Radial Case

2020
Journal Articles

Abstract

We investigate the stability and stabilization of the cubic focusing Klein-Gordon equation around static solutions on the closed ball in $\mathbb{R}^3$ . First we show that the system is linearly unstable near the static solution $u\equiv1$ for any dissipative boundary condition $u_t+au_ν=0,a∈(0,1)$ . Then by means of boundary controls (both open-loop and closed-loop) we stabilize the system around this equilibrium exponentially with rate less than $\frac{\sqrt 2}{2L} log \frac{1+a}{1-a}$ , which is sharp, provided that the radius of the ball $L$ satisfies $L≠tan\:L$ .

Official source

Graph Chat

Chat with Graph Search

Ask any question about EPFL courses, lectures, exercises, research, news, etc. or try the example questions below.

DISCLAIMER: The Graph Chatbot is not programmed to provide explicit or categorical answers to your questions. Rather, it transforms your questions into API requests that are distributed across the various IT services officially administered by EPFL. Its purpose is solely to collect and recommend relevant references to content that you can explore to help you answer your questions.

2020
Journal Articles

Abstract

Official source

Related concepts (10)

Racism

Racism is discrimination and prejudice towards people based on their race or ethnicity. Racism can be present in social actions, practices, or political systems (e.g. apartheid) that support the expression of prejudice or aversion in discriminatory practices. The ideology underlying racist practices often assumes that humans can be subdivided into distinct groups that are different in their social behavior and innate capacities and that can be ranked as inferior or superior.

Closed-loop controller

A closed-loop controller or feedback controller is a control loop which incorporates feedback, in contrast to an open-loop controller or non-feedback controller. A closed-loop controller uses feedback to control states or outputs of a dynamical system. Its name comes from the information path in the system: process inputs (e.g., voltage applied to an electric motor) have an effect on the process outputs (e.g., speed or torque of the motor), which is measured with sensors and processed by the controller; the result (the control signal) is "fed back" as input to the process, closing the loop.

Open-loop controller

In control theory, an open-loop controller, also called a non-feedback controller, is a control loop part of a control system in which the control action is independent of the "process output", which is the process variable that is being controlled. It does not use feedback to determine if its output has achieved the desired goal of the input command or process setpoint. There are many open-loop controls, such as on/off switching of valves, machinery, lights, motors or heaters, where the control result is known to be approximately sufficient under normal conditions without the need for feedback.