Rigorous Numerics for Partial Differential Equations: The Kuramoto—Sivashinsky Equation
نویسندگان
چکیده
منابع مشابه
Rigorous 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...
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Rigorous 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 کاملStochastic and Partial Differential Equations with Adapted Numerics 1
1 This is a draft. Comments and improvements are welcome.
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ژورنال
عنوان ژورنال: Foundations of Computational Mathematics
سال: 2001
ISSN: 1615-3375
DOI: 10.1007/s002080010010