APLIKASI SEMIGRUP OPERATOR LINEAR PADA PENYESELESAIAN MASALAH CAUCHY ABSTRAK DEGENERATE HOMOGEN

Abstract

In this article, we will investigate how to apply the linear operator semigroup to solve the abstract degenerate Cauchy problem. The problem is treated under  the assumption that the Hilbert space of the system can be written as a direct sum of  the kernel of M (KerM ) and the range of adjointM (RanM*). By certain assumptions this problem can be reduced into nondegenerate Cauchy problem. By assumptions the operator A is a infinitesimal generator, the canonic problem has a unique solution.  And then by using the particular operator, any solution of nondegenerate problem can be mapped to the solution of degenerate Cauchy problem.