Heriot-Watt Mathematics Report Series
HWM06-19, 21 Apr 2006
Hamiltonian PDEs
S B Kuksin
Abstract
In this work we discuss qualitative properties
of solutions for Hamiltonian partial differential equations in the
finite volume case. That is, when the space-variable $x$ belongs to a
finite domain and appropriate boundary conditions are specified on the
domain's boundary (or $x$ belongs to the whole space, but the equation
contains a potential term, where the potential growths to infinity as
$|x|\to\infty$, cf. below Example~\ref{ex2.4} in section~\ref{s33}).
Most of these properties have analogies in the classical
finite-dimensional Hamiltonian mechanics. In the infinite-volume case
properties of the equations become rather different due to the
phenomenon of radiation, and we do not touch them here.
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