Inertial Manifolds for the Kuramoto-sivashinsky Equation
نویسنده
چکیده
A new theorem is applied to the Kuramoto-Sivashinsky equation with L-periodic boundary conditions, proving the existence of an asymptotically complete inertial manifold attracting all initial data. Combining this result with a new estimate of the size of the globally absorbing set yields an improved estimate of the dimension, N ∼ L.
منابع مشابه
Evaluating the Dimension of an Inertial Manifold for the Kuramoto-sivashinsky Equation∗
The Kuramoto-Sivashinsky equation is a dissipative evolution equation in one space dimension which, despite its apparent simplicity, gives rise to a very rich dynamical behavior, as evidenced for instance by the study in [16], of its complicated set of stationary solutions and stationary and Hopf bifurcations. The large time behavior of the solutions is usually embodied by the attractor and the...
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