Group theoretic analysis of a class of boundary value problems for a nonlinear heat equation
Mathematical Physics
2012-02-06 v1 math.MP
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.
Keywords
Cite
@article{arxiv.1202.0705,
title = {Group theoretic analysis of a class of boundary value problems for a nonlinear heat equation},
author = {Sergii Kovalenko},
journal= {arXiv preprint arXiv:1202.0705},
year = {2012}
}
Comments
17 pages, 2 figures