Long-time dynamics of von Karman semi-flows with non-linear boundary/interior damping

By Igor D. Chueshov, Irena Lasiecka. 2007

74 citations recorded by the source corpus.

Abstract We study von Karman evolution equations with non-linear dissipation and with partially clamped and partially free boundary conditions. Two distinctive mechanisms of dissipation are considered: (i) internal dissipation generated by non-linear operator, and (ii) boundary dissipation generated by shear forces friction acting on a free part of the boundary. The main emphasis is given to the effects of boundary dissipation. Under suitable hypotheses we prove existence of a compact global attractor and finiteness of its fractal dimension. We also show that any solution is stabilized to an equilibrium and estimate the rate of the convergence which, in turn, depends on the behaviour at the origin of the functions describing the dissipation.

Subfields: Computational Theory and Mathematics, Computer Networks and Communications, Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/94ab51cd97c63ce2ee56556a6f3ebeeb0d611603

Citations in the corpus

• Existence and sharp decay rate estimates for a von Karman system with long memory (2015, unknown): “Starting with existence of weak solutions obtained by Faedo Galerkin methods [2,3], study of regularity of solutions [4,5] and of long time behavior subject to frictional or thermal damping [5,6]were natural topics for consideration.”