Results of Semigroup of Linear Equation Generating a Wave Equation
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.
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