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.

Google Scholar Search: links, citations and journal (if available)


Contact Details | 2006 Reports Index | Full Index