Finite dimensionality of the attractor for a semilinear wave equation with nonlinear boundary dissipation
Abstract
Long-time behavior of a semilinear wave equation with nonlinear boundary dissipation is considered. It is shown that weak solutions generated by the wave dynamics converge asymptotically to a finite dimensional attractor. Under the additional assumption that the set of stationary points is finite it is proved that every solution converges to some stationary point at an exponential rate. This result makes it possible to prove that the global attractor is exponential, i.e., it attracts every bounded set with exponential speed.
Publication Title
Communications in Partial Differential Equations
Recommended Citation
Chueshov, I., Eller, M., & Lasiecka, I. (2004). Finite dimensionality of the attractor for a semilinear wave equation with nonlinear boundary dissipation. Communications in Partial Differential Equations, 29 (11-12), 1847-1876. https://doi.org/10.1081/PDE-200040203
