Discontinuous Galerkin approximation of porous Fisher-Kolmogorov equations

We consider the generalized porous Fisher-Kolmogorov equations, which model several phenomena in population dynamics, as well as in chemical reactions. For these equations, we present new numerical high-order schemes, based on discontinuous Galerkin space discretizations and Runge-Kutta time stepping. These methods are capable to reproduce the main properties of the analytical solutions. We present some preliminary theoretical results and provide several numerical tests.