Dynamics for the stochastic nonlocal Kuramoto–Sivashinsky equation
نویسندگان
چکیده
منابع مشابه
Controlling roughening processes in the stochastic KuramotoSivashinsky equation
We present a novel control methodology to control the roughening processes of semilinear parabolic stochastic partial differential equations in one dimension, which we exemplify with the stochastic Kuramoto-Sivashinsky equation. The original equation is split into a linear stochastic and a nonlinear deterministic equation so that we can apply linear feedback control methods. Our control strateg...
متن کاملSpatial Analyticity on the Global Attractor for the KuramotoSivashinsky Equation
For the Kuramoto Sivashinsky equation with L-periodic boundary conditions we show that the radius of space analyticity on the global attractor is lowersemicontinuous function at the stationary solutions, and thereby deduce the existence of a neighborhood in the global attractor of the set of all stationary solutions in which the radius of analyticity is independent of the bifurcation parameter ...
متن کاملFront Propagation and Clustering in the Stochastic Nonlocal Fisher Equation
The nonlocal Fisher equation is a diffusion-reaction equation where the reaction has a linear birth term and a nonlocal quadratic competition, which describes the reaction between distant individuals. This equation arises in evolutionary biological systems, where the arena for the dynamics is trait space, diffusion accounts for mutations and individuals with similar traits compete, resulting in...
متن کاملHeteroclinic dynamics in the nonlocal parametrically driven nonlinear Schrödinger equation
Faraday waves are described, under appropriate conditions, by a damped nonlocal parametrically driven nonlinear Schrödinger equation. As the strength of the applied forcing increases this equation undergoes a sequence of transitions to chaotic dynamics. The origin of these transitions is explained using a careful study of a two-mode Galerkin truncation and linked to the presence of heteroclinic...
متن کاملSplitting methods for the nonlocal Fowler equation
We consider a nonlocal scalar conservation law proposed by Andrew C. Fowler to describe the dynamics of dunes, and we develop a numerical procedure based on splitting methods to approximate its solutions. We begin by proving the convergence of the well-known Lie formula, which is an approximation of the exact solution of order one in time. We next use the split-step Fourier method to approximat...
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: Journal of Mathematical Analysis and Applications
سال: 2007
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2006.07.091