Observability inequality and decay rate for wave equations with nonlinear boundary conditions

Abstract

We study a class of wave propagation problems concerning the nonlinearity of dynamic evolution for boundary material. We establish an observability inequality for the related linear system, and make a connection between the linear system and the original nonlinear coupled system. Also, we obtain the desired energy decay rate for the original nonlinear boundary value problem.

Keywords

• Nonlinear wave
• coupled boundary equations
• uniform decay rates
• observability inequality