• 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
ut = (k(u)ux)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.
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