Attracting Fixed Points for the Kuramoto-Sivashinsky Equation: A Computer Assisted Proof
نویسنده
چکیده
We present a computer assisted proof of the existence of several attracting fixed points for the Kuramoto–Sivashinsky equation ut = (u )x − uxx − νuxxxx, u(x, t) = u(x+ 2π, t), u(x, t) = −u(−x, t), where ν > 0. The method is general and can be applied to other dissipative PDEs.
منابع مشابه
Heteroclinic Connections in the Kuramoto-Sivashinsky Equation: a Computer Assisted Proof
On the example of a nite dimensional approximation of the Kuramoto-Sivashinsky equation we show how topological methods may be successfully used in computer assisted proofs of the existence of heteroclinic connections in ordinary diierential equations.
متن کاملcient algorithms for rigorous integration forward in time of dPDEs . Existence of globally attracting xed points of viscous Burgers equation with constant forcing , a computer assisted proof
The dissertation is divided into two separate parts. First part We propose an e cient and generic algorithm for rigorous integration forward in time of systems of equations originating from partial di erential equations written in the Fourier basis. By rigorous integration we mean a procedure, which operates on sets, and return sets which are guaranteed to contain the exact solution. The algori...
متن کاملRigorous Numerics for Dissipative Partial Differential Equations II. Periodic Orbit for the Kuramoto-Sivashinsky PDE-A Computer-Assisted Proof
We present a method of self-consistent a-priori bounds, which allows to study rigorously dynamics of dissipative PDEs. As an application present a computer assisted proof of an existence of a periodic orbit for the Kuramoto-Sivashinsky equation ut = (u )x− uxx− νuxxxx, u(t, x) = u(t, x + 2π), u(t, x) = −u(t,−x),
متن کاملRigorous Numerics for Partial Differential Equations: The Kuramoto-Sivashinsky Equation
We present a new topological method for the study of the dynamics of dissipative PDE’s. The method is based on the concept of the selfconsistent apriori bounds, which allows to justify rigorously the Galerkin projection. As a result we obtain a low-dimensional system of ODE’s subject to rigorously controlled small perturbation from the neglected modes. To this ODE’s we apply the Conley index to...
متن کاملSteady State Bifurcations for the Kuramoto-sivashinsky Equation - a Computer Assisted Proof
We apply the method of self-consistent bounds to prove the existence of multiple steady state bifurcations for Kuramoto-Sivashinski PDE on the line with odd and periodic boundary conditions.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- SIAM J. Applied Dynamical Systems
دوره 1 شماره
صفحات -
تاریخ انتشار 2002