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.

Traveling waves for degenerate diffusive equations on networks / Corli, Andrea; Ruvo, Lorenzo di; MALAGUTI, Luisa; Rosini, Massimiliano D.. - In: NETWORKS AND HETEROGENEOUS MEDIA. - ISSN 1556-1801. - 12:3(2017), pp. 339-370. [10.3934/nhm.2017015]

Traveling waves for degenerate diffusive equations on networks

MALAGUTI, Luisa;
2017

Abstract

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.
2017
set-2017
12
3
339
370
Traveling waves for degenerate diffusive equations on networks / Corli, Andrea; Ruvo, Lorenzo di; MALAGUTI, Luisa; Rosini, Massimiliano D.. - In: NETWORKS AND HETEROGENEOUS MEDIA. - ISSN 1556-1801. - 12:3(2017), pp. 339-370. [10.3934/nhm.2017015]
Corli, Andrea; Ruvo, Lorenzo di; MALAGUTI, Luisa; Rosini, Massimiliano D.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11380/1145649
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