PERLUASAN MASALAH CAUCHY ABSTRAK DEGENERATE THE GENERALIZATION OF DEGENERATE ABSTRACT CAUCHY PROBLEM

Hariyanto, Susilo, Lina Aryati

2015 | Tesis | FMIPA

In the first we will discuss about the alternative solution of nonhomogeneous abstract degenerate Cauchy problem by factorization method. This problem is defined in a Hilbert space which can be expressed as a direct sum of two subspaces in the Hilbert space. Both of them are mutually orthogonal. In the equation of homogeneous abstract degenerate, the operators are closed and densely defined. By using several certain assumptions and restriction to ? ? (Ker M) D(M) of domain operator M, the degenerate Cauchy problem can be reduced to nondegenerate problem. By another procedure, the nondegenerate Cauchy problem can be expressed in normal form which is called the alternative normal form. Moreover, by using a specific operator the solution of alternative normal form can be mapped to the solution of nonhomogeneous degenerate Cauchy problem. So we can solve the problem by factorization method. The reseach also investigate how to solve the generalization abstract degenerate Cauchy problem. This is a modification of previous reseach about the solution of nonhomogeneous abstract degenerate Cauchy problem in linear case. Here the generalization is meant the addition of a linear operator on the nonhomogeneous term’s. We will study two kind addition of a linear operator that are bounded or closed operator. By using several new assumptions, solution of generalization abstract degenerate Cauchy problem can be found by factorization method

Kata Kunci : Degenerate Cauchy problem; Nondegenerate Cauchy problem; Factorization method