A theorem on C_0 semigroups generated by a class of infinite dimensional Hamiltonian operators
Junjie Huang · 2006
The problem in which the infinite dimensional Hamiltonian operators generate semigroups is investigated,and a sufficient condition of generating semigroups is obtained for a class of infinite dimensional Hamiltonian operators.The results are applied to the infinite dimensional Hamiltonian operators generated by a class of mixed problems of hyperbolic PDE's,and it is showed that these operators generate semigroups.The correctness and effectiveness of the results are further demonstrated by Hille-Yosida's theorem.Besides,the expression of semigroup generated by an infinite dimensional Hamiltonian operator corresponding to a wave equation is given.