Group theoretic analysis of a class of boundary value problems for a nonlinear heat equation

2012/02/03 by Sergii Kovalenko, Kovalenko, Sergii
Mathematics · Physics and Astronomy · #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.MP

paper · pdf · doi:10.48550/arxiv.1202.0705

17 pages, 2 figures

arxiv created 2012/02/03 · arxiv updated 2012/02/06

Abstract

A definition of invariance in Lie's sense for a boundary value problem (BVP) with the basic evolution differential equations is proposed. A problem of group classification at a wide class of BVPs parameterized by arbitrary elements is formulated and an algorithm for its solution is also proposed. The group classification of a class of BVPs for an (1+1)--dimensional nonlinear heat equation arising from mathematical modeling of heat conduction in semi-infinite body is carried out. An example of invariant solution of a BVP from the class under study is presented.

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