# Results of Semigroup of Linear Equation Generating a Wave Equation

Open Access

- 9 October 2022
- journal article
- research article
- Published by Earthline Publishers in Earthline Journal of Mathematical Sciences
- Vol. 11 (1), 173-182
- https://doi.org/10.34198/ejms.11123.173182

##### 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

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