Semigrup Operator Linier Terbatas untuk Menyelesaikan Masalah Cauchy Abstrak

Abstract

The abstract Cauchy problem in the form of a linear system, x(t)=Tx(t),x(0)=x0,t≥0 with T is a bounded linear operator. The problem is a common form of linear system, x(t)=Ax(t),x(0)=x0,t≥0 with A is a square matrix having an inverse. Since the matrix has an inverse it can be formed into a bounded linear operator that satisfies semigroups properties. Each MCA formed into semigroups of bounded linear operator always has a unique solution,x(t)=eAtx0 for each tϵR.