Results of semigroup of linear operators generating a semilinear evolution equation in R^3

Abstract

In this paper, we present results of ω-order preserving partial contraction mapping generating a semilinear evolution equation in R^3. We consider a bounded domain ω with smooth boundary ω in R^3 and use the technique of semilinear equations with analytic semigroups to obtain a strong solution of the initial value problem. We showed that the operator A is symmetric and that A is the infinitesimal generator of a C_0-semigroup on L^2(ω). Finally we established that operator A is well defined, self adjoint and its the infinitesimal generator of an analytic semigroup.