SEMIGROUP THE SINE GORDON EQUATION

• Main Author: Budiartini Partiwi, Woro
• Format: Theses
• Language: Indonesia
• Subjects: Matematika
• Online Access: https://digilib.itb.ac.id/gdl/view/33852
• Institution: Institut Teknologi Bandung

Semigroup C0 is one of the methods used to show the Initial Value Problems (MNA) of dierential equations in Hilbert space are well posed. MNA in this abstract called Abstract Cauchy Problem. Semigrup is a family of linear operators fT(t) : t geq0g on Hilbert space H that satisfy semigroup nature, that is closed to the composition and has the identity element. Furthermore, if semigrup have derivatives at the point t = 0, then the derivative called a generator. In this case, Lummer Philips Theorem provide equivalent between the generator and semigroup. If semigroup involves negative parameter t, then the linear operator family fT????1(t) : t < 0g also form semigroup. In certain cases semigroup can be expanded into a group. Stone theorem gives equivalent between the generator group. Technically, Lummer Philips Theorem said the MNA is well posed if and only if the generator is the operator m-dissipative. Sine Gordon equation is non-linear equations or may be expressed as a linear pertuba- tion of non-linear equations. By Pertubation Theorem, an operator m- -dissipative added to the non linear nite factor, does not alter the nature of the operator m-dissipative. Thus, non-linear dierential equation is well posed. Application of semigrup applied to the Sine Gordon equation.