A model problem for groundwater flow with dynamic capillary pressure: stability of travelling waves Original Research Article

Modelling vertical nonsteady groundwater flow with dynamic capillary pressure leads to a nonlinear diffusion–convection equation extended with a nonlinear third order term with two space derivatives and one time derivative. We consider the special case in which the original equation is the Burgers’ equation and the third order term is linear. We investigate stability of travelling wave solutions of the resulting pseudo-parabolic Burgers’ equation, for which we first obtain well-posedness results.