ON A CONSTRUCTION OF INERTIAL MANIFOLDS FOR A CLASSOF SECOND ORDER IN TIME EVOLUTION EQUATIONS
Citation：
WANG Zongxin.ON A CONSTRUCTION OF INERTIAL MANIFOLDS FOR A CLASSOF SECOND ORDER IN TIME EVOLUTION EQUATIONS[J].Chinese Annals of Mathematics B,1999,20(3):271~278
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Authors：
WANG Zongxin;
Abstract：
Inertial manifolds for a class of second order in time dissipative
equations are constructed. The author also proves an asymptotic
completeness property for the inertial manifolds and characterizes
the inertial manifolds as the set of trajectories whose growth is at
most of order $O(e^{-\mu t})$ for some $\mu >0$. As applications,
a
nonlinear wave equation and a problem of nonlinear oscillations of a
shallow shell are considered.
