Stationary fronts and pulses for multistable equations with saturating diffusion

We deal with stationary solutions of a reaction-diffusion equa-tion with flux-saturated diffusion and multistable reaction term, in de-pendence on a positive parameter epsilon. Motivated by previous numerical results obtained by A. Kurganov and P. Rosenau (Nonlinearity, 2006), we investigate stationary solutions of front and pulse-type and discuss their qualitative features. We study the limit of such solutions for epsilon -> 0, showing that, in spite of the wide variety of profiles that can be con-structed, there is essentially a unique configuration in the limit for both stationary fronts and pulses. We finally discuss some variational features that include the case where the solutions having continuous energy may not be global minimizers of the associated action functional.