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

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

2012-02-03

arxiv.org/abs/1202.0705v1

Physics

Mathematical Physics

17 pages, 2 figures

Scientific paper

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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