1202.0705 (Sergii Kovalenko)

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

Sergii Kovalenko

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.

View original: http://arxiv.org/abs/1202.0705