Inertial manifolds for a Smoluchowski equation on a circle
نویسندگان
چکیده
The existence of inertial manifolds for a Smoluchowski equation—a nonlinear and nonlocal Fokker–Planck equation which arises in the modelling of colloidal suspensions—is investigated. The difficulty due to first-order derivatives in the nonlinearity is circumvented by a transformation. Mathematics Subject Classification: 35Kxx, 70Kxx
منابع مشابه
Inertial Manifolds for a Smoluchowski Equation on the Unit Sphere
The existence of inertial manifolds for a Smoluchowski equation – a nonlinear Fokker-Planck equation on the unit sphere which arises in modeling of colloidal suspensions – is investigated. A nonlinear and nonlocal transformation is used to eliminate the gradient from the nonlinear term.
متن کاملFinite-dimensional Description of the Long-term Dynamics for the 2d Doi-hess Model for Liquid Crystalline Polymers in a Shear Flow
The existence of inertial manifolds for a Smoluchowski equation arising in the 2D Doi-Hess model for liquid crystalline polymers subjected to a shear flow is investigated. The presence of a non-variational drift term complicates the dynamics dramatically from the gradient case in which the it is characterized solely by the steady states. Several transformations are used in order to bring the eq...
متن کاملInertial manifolds under multistep discretization
Finite-dimensional inertial manifolds attract solutions to a nonlinear parabolic diierential equation at an exponential rate. In this paper inertial manifolds for multistep discretizations of such equations are studied. We provide an existence result for inertial manifolds under multistep discretization and show that these inertial manifolds converge to the inertial manifold of the original equ...
متن کاملApproximate inertial manifolds for the pattern formation Cahn-Hilliard equation
An approximate inertial manifold for an évolution équation is a finite dimensional smooth manifold such that the orbits enter, after a transient time, a very thin neighbourhood of the manifold In this paper, we consider the Cahn-Hilliard équation and we present a method which allows to construct several approximate inertial manifolds providing better and better order approximations to the orbit...
متن کاملGlobal Dissipativity and Inertial Manifolds for Diffusive Burgers Equations with Low-Wavenumber Instability
Global well-posedness, existence of globally absorbing sets and existence of inertial manifolds is investigated for a class of diffusive Burgers equations. The class includes diffusive Burgers equation with nontrivial forcing, the Burgers-Sivashinsky equation and the QuasiStedy equation of cellular flames. The global dissipativity is proven in 2D for periodic boundary conditions. For the proof ...
متن کامل