Irreducibility of Kuramoto-Sivashinsky equation driven by degenerate noise
نویسندگان
چکیده
In this paper, we study irreducibility of Kuramoto-Sivashinsky equation which is driven by an additive noise acting only on a finite number Fourier modes. order to obtain the irreducibility, first investigate approximate controllability finite-dimensional force, proof based Agrachev-Sarychev type geometric control approach. Next, continuity solving operator for deterministic equation. Finally, combining with operator, establish
منابع مشابه
Feedback control of the Kuramoto – Sivashinsky equation
This work focuses on linear finite-dimensional output feedback control of the Kuramoto–Sivashinsky equation (KSE) with periodic boundary conditions. Under the assumption that the linearization of the KSE around the zero solution is controllable and observable, linear finite-dimensional output feedback controllers are synthesized that achieve stabilization of the zero solution, for any value of ...
متن کاملExact Solutions of the Generalized Kuramoto-Sivashinsky Equation
In this paper we obtain exact solutions of the generalized Kuramoto-Sivashinsky equation, which describes manyphysical processes in motion of turbulence and other unstable process systems. The methods used to determine the exact solutions of the underlying equation are the Lie group analysis and the simplest equation method. The solutions obtained are then plotted.
متن کاملInertial Manifolds for the Kuramoto-sivashinsky Equation
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.
متن کاملOn the Stochastic Kuramoto-Sivashinsky Equation
In this article we study the solution of the Kuramoto–Sivashinsky equation on a bounded interval subject to a random forcing term. We show that a unique solution to the equation exists for all time and depends continuously on the initial data.
متن کاملHopping behavior in the Kuramoto-Sivashinsky equation.
We report the first observations of numerical "hopping" cellular flame patterns found in computer simulations of the Kuramoto-Sivashinsky equation. Hopping states are characterized by nonuniform rotations of a ring of cells, in which individual cells make abrupt changes in their angular positions while they rotate around the ring. Until now, these states have been observed only in experiments b...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: ESAIM: Control, Optimisation and Calculus of Variations
سال: 2022
ISSN: ['1262-3377', '1292-8119']
DOI: https://doi.org/10.1051/cocv/2022014