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

Jie Liu, Junjie Huang, Jiahui Yu, Jingying Gao and Mohammad W. Alomari

Journal of Mathematics, 2024, vol. 2024, 1-9

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.

Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:6621165

DOI: 10.1155/2024/6621165

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