Stationary fronts and pulses for multistable equations with saturating diffusion

We deal with stationary solutions of a reaction-diffusion equation with flux-saturated diffusion and multistable reaction term, in dependence on a positive parameter ε. 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 ε→0, showing that, in spite of the wide variety of profiles that can be constructed, 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.