Group classification of systems of diffusion equations

Abstract

Group classification of a class of systems of diffusion equations is carried out. Arbitrary elements that appear in the system depend on two variables. All forms of the arbitrary elements that provide additional Lie symmetries are determined. Equivalence transformations are used to simplify the analysis. Examples of similarity reductions are presented. Copyright

Lie symmetries of a system arising in plasma physics

“…Classification of Lie symmetries and potential symmetries for the system are open problems. Similar problems have been considered in other works …”

“…Lie symmetries can also be used to solve initial or/and boundary value problems (see, for example, the other works) . There is a continuing interest in deriving Lie symmetries for systems of partial differential equations in the last few years …”

Lie symmetry analysis of Burgers‐type systems

“…In the present problem, the arbitrary elements f and k depend on 2 variables which make the classification even more difficult than the usual ones. Similar problem where there exist 2 arbitrary elements depending in 2 variables was considered recently in Kontogiorgis and Sophocleous . Another good example, is Stepanova, where certain results of group classification of complex 3‐dimensional diffusion‐type equations are presented.…”

Symmetry of heat and mass transfer equations in case of dependence of thermal diffusivity coefficient either on temperature or concentration

“…The solution of group classification problem for the heat and mass transfer equations taking into account the Dufour effect and/or the Soret effect without convection terms is presented in Stepanova, respectively. The symmetries of the system of evolution equation with 2 arbitrary functions are found in Kontogiorgis and Sophocleous …”