The Problem Of Infinite Dimensional Hamiltonian Operators Generate C₀ Semigroups

In this thesis, the problem of infinite dimensional Hamiltonian operators generate C₀ semigroups is investigated, and some sufficient conditions for upper-triangular infinite dimensional Hamiltonian operators and the oblige diagonal defined infinite dimensional Hamiltonian operators generate C₀ semigroups are given. The results are applied to the infinite dimensional Hamiltonian operators generated by a class of initial valve problem with constant coefficients of parabolic PDE, initial value problem of unbounded string vibration equation, boundary value problem of single hyperbolic differential equations. It is showed that these operators generate semigroups, and that the correctness and effectiveness of the results are demonstrated by Hille-Yosida's theorem. Moreover, the expressions of semigroups generated by these infinite dimensional Hamiltonian operators are presented, and the corresponding solutions of theses Cauchy problems are given. The results are identical with the results solved by the method for solving general solutions.