Rigorous Numerics for Dissipative Partial Differential Equations II. Periodic Orbit for the Kuramoto-Sivashinsky PDE-A Computer-Assisted Proof
نویسنده
چکیده
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),
منابع مشابه
Rigorous Numerics for Dissipative PDEs III. An effective algorithm for rigorous integration of dissipative PDEs
We describe a Lohner-type algorithm for rigorous integration of dissipative PDEs. Using it for the Kuramoto-Sivashinsky PDE on the line with odd and periodic boundary conditions we give a computer assisted proof the existence of multiple periodic orbits.
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 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 کاملIntegration of Dissipative Partial Differential Equations: A Case Study
We develop a computer-assisted technique for constructing and analyzing orbits of dissipative evolution equations. As a case study, the methods are applied to the Kuramoto–Sivashinski equation, for which we prove the existence of a hyperbolic periodic orbit.
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
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Foundations of Computational Mathematics
دوره 4 شماره
صفحات -
تاریخ انتشار 2004