Semigroup Generation Theorems of Anti‐Triangular Operator Matrices and Their Application

Abstract

This paper deals with the semigroup generation of anti‐triangular operator matrices M with unbounded entries in Hilbert space. Based on the space decomposition, some necessary and sufficient conditions are given for M to generate contraction semigroups. In addition, the anti‐triangular differential system, converted from the damping wave equation, is used to explain our work, and it is proved that the corresponding anti‐triangular operator matrix satisfies the conditions and generates a contraction semigroup.