Olena Vaneeva (Institute of Mathematics of the NAS of Ukraine, Kyiv)

Group analysis and conservation laws of variable coefficient reaction-diffusion equations

Abstract:
We exhaustively describe an equivalence groupoid of the class of reaction-diffusion equations $$ f(x)u_t=(g(x)A(u)u_x)_x+h(x)B(u), \quad fgA\neq0, $$ were $f$, $g$, $h$, $A$ and $B$ are arbitrary smooth functions of their variables. A classification of Lie symmetries and conservation laws of this class is carried out using the method of partition of the class into normalized subclasses.

The results are obtained jointly with R. Popovych and C. Sophocleous.