Asymptotic stability and blow up for a semilinear damped wave equation with dynamic boundary conditions

作者：Gerbi S^*; Said Houari B

来源：Nonlinear Analysis-Theory Methods & Applications, 2011, 74(18): 7137-7150.

DOI：10.1016/j.na.2011.07.026

• Damped wave equations
• Stable and unstable set
• Global solutions
• Blow up
• Kelvin-Voigt damping
• Dynamic boundary conditions

In this paper we consider a multi-dimensional wave equation with dynamic boundary conditions, related to the Kelvin-Voigt damping. Global existence and asymptotic stability of solutions starting in a stable set are proved. Blow up for solutions of the problem with linear dynamic boundary conditions with initial data in the unstable set is also obtained.

• 出版日期2011-12