# infinite dimensional hamiltonian system

infinite dimensional hamiltonian system

An infinite dimensional Hamiltonian system takes the form

 $(IHS)\;\;\left\{\begin{array}[]{rll}\partial_{t}u-\Delta_{x}u&=H_{v}(t,x,u,v)&% \\ -\partial_{t}v-\Delta_{x}v&=H_{u}(t,x,u,v)&\forall(t,x)\in\mathbb{R}\times% \Omega\end{array}\right.$

where $\Omega\subset{\mathbb{R}}^{N}$ is a smoothly bounded domain, $H\in\mathcal{C}^{1}(\mathbb{R}\times\overline{\Omega}\times\mathbb{R}^{2},% \mathbb{R})$.

Title infinite dimensional hamiltonian system InfiniteDimensionalHamiltonianSystem1 2013-03-11 19:28:50 2013-03-11 19:28:50 linor (11198) (0) 1 linor (0) Definition