On the attractor for a semilinear wave equation with critical exponent and nonlinear boundary dissipation
Abstract
Long time behavior of a semilinear wave equation with nonlinear boundary dissipation and critical exponent is considered. It is shown that weak solutions generated by the wave dynamics converge asymptotically to a global and compact attractor. In addition, regularity and structure of the attractor are discussed in the paper. While this type of results are known for wave dynamics with interior dissipation this is, to our best knowledge, first result pertaining to boundary and nonlinear dissipation in the context of global attractors and their properties.
Publication Title
Communications in Partial Differential Equations
Recommended Citation
Chueshov, I., Eller, M., & Lasiecka, I. (2002). On the attractor for a semilinear wave equation with critical exponent and nonlinear boundary dissipation. Communications in Partial Differential Equations, 27 (9-10), 1901-1951. https://doi.org/10.1081/PDE-120016132
