Heat conduction in anisotropic media: Nonlinear self-adjointness and   conservation laws
  Nonlinear self-adjointness of the anisotropic nonlinear heat equation is investigated. Mathematical models of heat conduction in anisotropic media with a source are considered and a class of self-adjoint models is identified. Conservation laws corresponding to the symmetries of the equations in question are computed. 
Nail H. Ibragimov and Elena D. Avdonina
math-ph math.MP