Persamaan Diferensial Linear Boltzmann

SUGANDHA, Agus, Dr. Widodo, MS

2005 | Tesis | S2 Matematika

Didalam tesis ini akan dibahas tentang persamaan diferensial linear Boltzmann beserta solusi dan sifat-sifatnya. Tujuan utama penelitian ini adalah mempelajari proses terbentuknya persamaan diferensial linear Boltzmann dan solusinya. Serta menganalisa sifat-sifat solusi persamaan diferensial linear Boltzmann, masalah eksistensi, dan ketunggalan solusinya. Solusi dari persamaan diferensial linear Boltzmann ini merupakan suatu titik tetap (fixed point) dari operator Markov. Pada bagian akhir dari tesis ini akan diperkenalkan persamaan diferensial linear Tjon-Wu yang merupakan kasus khusus dari persamaan diferensial linear Boltzmann .

In this thesis I would like to discuss the Boltzmann linear diferential equation with its solution and properties. The main objective of this research is to study the process of how the Boltzmann linear diferential equation is formed and its solution. Futhermore, I would also like to analize the solution properties of Boltzmann linear diferential equation, existence and uniqueness. The solution from this Boltzmann linear diferential equation is fixed point from Markov operator. In the last part of this thesis, I would introduce the Tjon-Wu linear diferential equation which is special case of the Boltzmann linear diferential equation. Measure and Lebesgue Integral are basic theory for the discussion of this study.

Kata Kunci : Persamaan Diferensial Linear Boltzmann,Sifat,sifat Solusi,The Boltzmann linear diferential equation, Markov operator, fixed point, the Tjon-Wu linear diferential equation