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Invariant manifold with complete foliations and chaotification analysis for a kind of PDEs with boundary coupling. (English) Zbl 1185.37160

Summary: We are concerned with the existence of invariant manifolds and complete foliations for a class of PDEs with boundary coupling. Some new form of gap relative coupling and inequality conditions are obtained. Further, we prove the topological equivalence of the flows in the respective attractors between the system and its spatial discretization system (an ODE system). Finally, the chaotification of the system is discussed through an example and simulation is generated to illustrate the theoretical results.

MSC:

37L25 Inertial manifolds and other invariant attracting sets of infinite-dimensional dissipative dynamical systems
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
35Q53 KdV equations (Korteweg-de Vries equations)
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