Traveling waves for degenerate diffusive equations on networks

Andrea D Corli (1) , Lorenzo Di Ruvo (2) , Luisa D Malaguti (2) , Massimiliano D. Rosini (3)

1 UniFE - Università degli Studi di Ferrara = University of Ferrara
2 UNIMORE - Università degli Studi di Modena e Reggio Emilia = University of Modena and Reggio Emilia
3 Instytut Matematyki = Institute of Mathematics [Lublin]

In this paper we consider a scalar parabolic equation on a star graph; the model is quite general but what we have in mind is the description of traffic flows at a crossroad. In particular, we do not necessarily require the continuity of the unknown function at the node of the graph and, moreover, the diffusivity can be degenerate. Our main result concerns a necessary and sufficient algebraic condition for the existence of traveling waves in the graph. We also study in great detail some examples corresponding to quadratic and logarithmic flux functions, for different diffusivities, to which our results apply.

Mots clés: AMS Subject Classification: 35K65; 35C07; 35K55; 35K57 Keywords: Parabolic equations; wavefront solutions; traffic flow on networks

Domaines: Equations aux dérivées partielles [math.AP]

Andrea D Corli, Lorenzo Di Ruvo, Luisa D Malaguti, Massimiliano D. Rosini. Traveling waves for degenerate diffusive equations on networks. 2017. ⟨hal-01446533⟩