On the Finiteness of the Number of Determining Elements for von Karman Evolution Equations
Igor Dmitrievich Chueshov · Mathematical Methods in the Applied Sciences · 1997
We prove the existence of a wide collection of finite sets of functionals that completely determine the long-time behaviour of strong solutions to the von Karman evolution equations. This collection contains finite sets of determining modes, nodes and local volume averages. The approach presented relies on the concept of a completeness defect for a set of linear functionals and it involves some ideas from abstract approximation theory. Our method is general enough and also can be applied to other non-linear partial differential equations which are of second order in time. © 1997 B. G. Teubner Stuttgart–John Wiley & Sons Ltd.