### Results of Semigroup of Linear Equation Generating a Wave Equation

J. B. Omosowon, A. Y. Akinyele, O. Y. Saka-Balogun
Published: 9 October 2022

Abstract: In this paper, we present results of $\omega$-order preserving partial contraction mapping generating a wave equation. We use the theory of semigroup to generate a wave equation by showing that the operator $\begin{pmatrix} 0 & I\\ \Delta & 0 \end{pmatrix},$ which is $A,$ is the infinitesimal generator of a $C_0$-semigroup of operators in some appropriately chosen Banach of functions. Furthermore we show that the operator $A$ is closed, unique and that operator $A$ is the infinitesimal generator of a wave equation.
Keywords: $\omega$-$OCP_n$ / evolution equation / $C_0$-semigroup / wave equation

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