(2+1) Boyutlu difüzyon denkleminin eşdeğerlik grupları

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.

Equivalence groups of (2+1) dimensional diffusion equation

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.

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