(2+1) Boyutlu difüzyon denkleminin eşdeğerlik grupları

Year 2017, , 1133 - 1139, 01.12.2017

Saadet Özer

https://doi.org/10.16984/saufenbilder.279668

Abstract

Bir diferansiyel denklemler grubu keyfi fonksiyonlar,
parametreler içeriyorsa, elimizde aynı yapıda diferansiyel denklemler ailesi
var demektir. Klasik fiziğin hemen hemen tüm alan denklemleri, içerdiği
parametrelerin farklı yapıları  için,
değişik malzemeleri temsil eder. Eşdeğerlik grupları, verilen bir diferansiyel
denklem ailesini değişmez bırakan dönüşüm grupları olarak tanımlanır. Bu
nedenle diferansiyel denklem ailelerinin eşdeğerlik grupları, aynı aileye ait,
farklı denklemler arası ilişkileri inceleme açısından önemli bir çalışma
alanıdır. Bu çalışmada, lineer olmayan 
difüzyon denklemin eşdeğerlik grupları, Lie grupları uygulaması
çerçevesinde incelenmiş ve sonuçlar tartışılmıştır. 

Keywords

Eşdeğerlik Grupları, Lie Grupları, difüzyon denklemi

Equivalence groups of (2+1) dimensional diffusion equation

Abstract

If a given set of differential equations contain some
arbitrary functions, parameters, we have in fact a family of sets of equations
of the same structure. Almost all field equations of classical physichs have
this property, representing different materials with various paramaters.  Equivalence groups are defined as the group
of transformations which leave a given family of differential equations
invariant. Therefore, equivalence group of family of differential equations is
an important area within the framework of the relations between different
equations of the same family. In this work the equivalence groups  of nonlinear diffusion equation are
investigated as application of Lie groups and their results are discussed. 

Keywords

Equivalence groups, Lie groups, Diffusion equation

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