CO−SEMIGROUPS OF CONTRADICTION ON BANACH SPACES AND APPLICATIONS
ABSTRACT
In this study, we focus on the properties of a Banach space denoted by X and an unbounded linear operator A, defined on a subset D(A) of X and mapping to X. Our main objective is to investigate the concept of a C0-semigroup of contractions on X, which is a family of bounded linear operators that evolves over time. We present two characterizations of A, known as the Hille-Yosida and Lumer Phillips characterizations, which describe A as the infinitesimal generator of the C0-semigroup on X.
Furthermore, we explore the application of C0-semigroups to partial differential equations with boundary conditions. By employing the C0-semigroup approach, we aim to analyze the behavior and solutions of these equations in a systematic manner. This framework provides a valuable tool for studying the dynamics and evolution of various physical and mathematical systems described by partial differential equations.
Through our investigation, we contribute to the understanding of C0-semigroups and their connection to unbounded linear operators in Banach spaces. Additionally, we provide insights into the application of this framework to partial differential equations, offering a promising avenue for further research in the field.
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