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July  1995, 1(3): 421-448. doi: 10.3934/dcds.1995.1.421

Approximate inertial manifolds of exponential order

Ricardo Rosa 1,

1. 

The Institute for Scientific Computing & Applied Mathematics, 618 E. Third St., Indiana University, Bloomington, IN 47405, United States

Received  February 1995 Published  May 1995

A fairly general class of nonlinear evolution equations with a self-adjoint or non self-adjoint linear operator is considered, and a family of approximate inertial manifolds (AIMs) is constructed. Two cases are considered: when the spectral gap condition (SGC) is not satisfied and an exact inertial manifold is not known to exist the construction is such that the AIMs have exponential order, while when the SGC is satisfied (and hence there exists an exact inertial manifold) the construction is such that the AIMs converge exponentially to the exact inertial manifold.
Keywords: approximate inertial manifolds, nonlinear evolution equations., self-adjoint linear operator.
Mathematics Subject Classification: 37L05, 37L25, 35Q3.
Citation: Ricardo Rosa. Approximate inertial manifolds of exponential order. Discrete and Continuous Dynamical Systems, 1995, 1 (3) : 421-448. doi: 10.3934/dcds.1995.1.421
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