Finite dimensionality and regularity of attractors for a 2-D semilinear wave equation with nonlinear dissipation
We consider a semilinear wave equation, defined on a two-dimensional bounded domain Ω, with a nonlinear dissipation. Our main result is that the flow generated by the model is attracted by a finite dimensional global attractor. In addition, this attractor has additional regularity properties that depend on regularity properties of nonlinear functions in the equation. To our knowledge this is a first result of this type in the context of higher dimensional wave equations. © 2002 Elsevier Science (USA). All rights reserved.
Journal of Mathematical Analysis and Applications
Lasiecka, I., & Ruzmaikina, A. (2002). Finite dimensionality and regularity of attractors for a 2-D semilinear wave equation with nonlinear dissipation. Journal of Mathematical Analysis and Applications, 270 (1), 16-50. https://doi.org/10.1016/S0022-247X(02)00006-9