The Structure of Lie Algebras and the Classification Problem for Partial Differential Equations

P. Basarab-Horwath, V. Lahno, R. Zhdanov

The present paper solves completely the problem of the group classification of nonlinear heat-conductivity equations of the form\ $u_t=F(t,x,u,u_x)u_{xx}+G(t,x,u,u_x)$. We…