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.

Results of Semigroup of Linear Operators Generating a General Class of Semilinear Initial Value Problems

“…Omosowon et al [10], established a regular weak*-continuous semigroup of linear operators, and also in [9], Omosowon et al, obtained a quasilinear equations of evolution on semigroup of linear operator.reversing partial contraction mapping generating a differential operator. Omosowon et al [12], deduced results of semigroup of linear equation generating a wave equation. Pazy [14], presented asymptotic behavior of the solution of an abstract evolution and some applications and also in [15], obtained a class of semi-linear equations of evolution.…”

The non-homogeneous Cauchy problem of semigroup of linear operators

“…Massit and Rossafi [11], obtained results equal-norm parseval continuous k-frames in Hilbert spaces. Omosowon et al [12] derived the outcomes of a semigroup of linear equations that produced a wave equation. Rauf et al [13], established some results of stability and spectra properties on semigroup of linear operator.…”