Lie symmetries of nonlinear boundary value problems

Details Lie symmetries of nonlinear boundary value problems Lie symmetries of nonlinear boundary value problems

2010-12-27

arxiv.org/abs/1012.5606v1

Physics

Mathematical Physics

21 pages, 2 figures

Scientific paper

Nonlinear boundary value problems (BVPs) by means of the classical Lie symmetry method are studied. A new definition of Lie invariance for BVPs are proposed by the generalization of existing those on much wider class of BVPs. The class of two-dimensional nonlinear boundary value problem, modeling the process of melting and evaporation of metals, is studied in details. Using the definition proposed, all possible Lie symmetries and the relevant reductions (with physical meaning) to BVPs for ordinary differential equations are constructed. An example how to construct exact solution of the problem with correctly-specified coefficients is presented and compared with the results of numerical simulations published earlier.

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