| Abstract: |
| We consider a system of two coupled reaction--diffusion equations in which one component is governed by doubly degenerate diffusion. These systems do not preserve the total mass, separating them from standard scalar reaction-diffusion equations.
We investigate the existence and qualitative properties of wavefront solutions, namely profiles that propagate with constant speed and are represented by a pair of strictly monotone functions. Using a combination of shooting techniques and fixed-point arguments, we derive conditions ensuring the existence of wavefronts and obtain estimates for threshold speeds.
We also address the regularity of the wavefront profiles and discuss the possible occurrence of sharp wavefronts arising from diffusion degeneracy.
The model arises in the study of the spatio-temporal evolution of bacterial colonies growing on nutrient-rich agar substrates.
Joint work with L.~Malaguti, V.~Taddei (University of Modena and Reggio Emilia), and E.~Mu\~noz-Hern\`andez (Complutense University of Madrid). |
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