We consider the two-dimensional diffusion-advection equation ut = Duyy - frac(d k, d u) ux. We present the classification of Lie symmetries of this equation. For the case k(u) = u2 we give the complete list of similarity solutions. Exact and numerical solutions are obtained.
- Diffusion-advection equations
- Exact solutions
- Lie symmetries
- Numerical solutions
- Similarity solutions