In this work we investigate the phenomena of pattern formation and wave propagation for a reaction–diffusion system with nonlinear diffusion. We show how cross-diffusion destabilizes uniform equilibrium and is responsible for the initiation of spatial patterns. Near marginal stability, through...

Nonlinear diffusion processes can give rise to shock wave type solutions. These solutions are usually derived from the application of similarity methods since general solutions to the relevant partial differential equations are not known. We consider the Boltzmann problem and construct an exact...