Heriot-Watt Mathematics Report Series
HWM99-73, 3 February 2000
A center manifold theorem for semilinear hyperbolic equations
A Shirikyan and L R Volevich
Abstract
An infinite-dimensional center manifold is constructed for a semilinear
hyperbolic equation of high order. It is proved that this manifold is locally
invariant under the action of the solving operator and exponentially
attracts all the solutions that are uniformly bounded on the
positive or negative half-line. A reduction principle according to which the
dynamics on the center manifold can be described by a lower order equation
is established.
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