• LIE SYMMETRIES OF NONLINEAR DIFFUSION EQUATIONS WITH CONVECTION TERM

Abstract

In the present paper, we consider nonlinear diffusion equations with convection term of the form

u_{t =} (k(u)u_x)_x + q(u), q(u) ≠ 0                                                                                                                                             (1)

where u = u(x, t) is the unknown function and k(u),  q(u) are arbitrary smooth functions.

Equation (1) generalizes a great number of the well-known nonlinear second-order evolution equations, describing various processes in physics, chemistry, biology. Apart from their intrinsic theoretical interest, the equations of the type (1) are used to model a wide variety of phenomena in physics, engineering, chemistry, biology etc.