DIFFERENTIABILITY OF PARABOLIC SEMI-FLOWS IN Lp-SPACES AND INERTIAL MANIFOLDS
نویسنده
چکیده
We consider the semi-flow defined by semi-linear parabolic equations in Lp-spaces and study the differentiable dependence on the initial data. Together with a spectral gap condition this implies existence of inertial manifolds in arbitrary space dimensions. The spectral gap condition is satisfied by the Laplace-Beltrami operator for a class of manifolds. The simplest examples are products of spheres.
منابع مشابه
Attractors and Inertial Manifolds for Finite Diierence Approximations of the Complex Ginzburg{landau Equation
A semi{discrete spatial nite diierence approximation and two fully discrete nite diierence approximations to the complex Ginzburg{Landau equation are considered in this paper. The existence of an inertial manifold is proved inside a discrete H 1 absorbing ball for the semi{discrete approximation by showing certain spectral properties hold for the linear operator and certain Lipschitz properties...
متن کاملReduced Order Control based on Approximate Inertial Manifolds
A reduced-order method based on approximate inertial manifolds is applied to optimal control problems in infinite-dimensional state spaces. A detailed analysis of the method is given for the linear quadratic regulator problem. The method can also be applied to higher-order control systems with an appropriate decomposition of the state space in terms of slow and fast exponential decay.
متن کاملDispersive Mixed-order Systems in L-sobolev Spaces and Application to the Thermoelastic Plate Equation
We study dispersive mixed-order systems of pseudodifferential operators in the setting of Lp-Sobolev spaces. Under the weak condition of quasihyperbolicity, these operators generate a semigroup in the space of tempered distributions. However, if the basic space is a tuple of Lp-Sobolev spaces, a strongly continuous semigroup is in many cases only generated if p = 2 or n = 1. The results are app...
متن کاملDiscontinuous Galerkin Methods for Friedrichs Systems with Irregular Solutions
Discontinuous Galerkin Methods for Friedrichs Systems with Irregular Solutions Max Jensen Doctor of Philosophy Corpus Christi College Michaelmas Term 2004 This work is concerned with the numerical solution of Friedrichs systems by discontinuous Galerkin finite element methods (DGFEMs). Friedrichs systems are boundary value problems with symmetric, positive, linear first-order partial differenti...
متن کاملLearning how to play Nash, potential games and alternating minimization method for structured nonconvex problems on Riemannian manifolds
In this paper we consider minimization problems with constraints. We show that if the set of constraints is a Riemannian manifold of non positive curvature and the objective function is lower semicontinuous and satisfies the Kurdyka-Lojasiewicz property, then the alternating proximal algorithm in Euclidean space is naturally extended to solve that class of problems. We prove that the sequence g...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1997