Controllability for a Wave Equation with Moving Boundary
Controllability for a Wave Equation with Moving Boundary
We investigate the controllability for a one-dimensional wave equation in domains with moving boundary. This model characterizes small vibrations of a stretched elastic string when one of the two endpoints varies. When the speed of the moving endpoint is less than<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mn>1</mml:mn><mml:mo>-</mml:mo><mml:mn>1</mml:mn><mml:mo>/</mml:mo><mml:msqrt><mml:mi>e</mml:mi></mml:msqrt></mml:math>, by Hilbert uniqueness method, sidewise energy estimates …