Abstract:
This thesis presents a preliminary study of symmetry analysis of a class of nonlinear heat equations of the formH : ut = f (x,ux)uxx+g(x,ux). We first review the notions related to symmetry analysis of differential
equations and then followed by examples that are relevant in the appli
cations. The preliminary study of the class of nonlinear heat equations
includes the computation of the equivalence group, the equivalence al
gebra and the analysis of the determining equations of equation from
the class under study. Using the direct method, all equivalence transformations connecting two equations from the class H were obtained. These transformations preserve the equations of the class and they are
projectable to the space of variables and arbitrary elements. The class
under study is not normalized. The infinitesimal counterparts of the
one parameter group for this class was computed and the commuta
tion relations of the vector fields spanning the maximal Lie invariance
Lie algebra was presented. The investigation and analysis of the de
termining equations for Lie symmetries of an equation from the class H lead to the expression of the maximal kernel invariance Lie algebra for equations from the class H. It is shown there that this Lie algebra is finite-dimensional, whereas the dimension of the linear span of the
maximal Lie invariance algebra is infinite.
