Finite dimensionality and compactness of attractors for von Karman equations with nonlinear dissipation


Asymptotic behaviour of dynamics governed by PDE system describing nonlinear vibrations of a shell immersed in a supersonic gas is considered. The undelying dynamics is modeled by a nonlinear hyperbolillike shell equation with a nonlinear dissipation. It is shown that all finite energy ("weak") solutions converge to a global, compact attractor which is also finite-dimensional.

Publication Title

Nonlinear Differential Equations and Applications