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EnglishIn 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.
| Data di pubblicazione: | 2017 | |
| Titolo: | Traveling waves for degenerate diffusive equations on networks | |
| Autori: | Corli, Andrea; Ruvo, Lorenzo di; Malaguti, Luisa; Rosini, Massimiliano D. | |
| Rivista: | NETWORKS AND HETEROGENEOUS MEDIA | |
| Keywords: | Parabolic equations; Traffic flow on networks; Wavefront solutions | |
| Abstract in inglese: | 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. | |
| Digital Object Identifier (DOI): | 10.3934/nhm.2017015 | |
| Handle: | http://hdl.handle.net/11392/2379524 | |
| Appare nelle tipologie: | 03.1 Articolo su rivista |
File in questo prodotto:
| File | Descrizione | Tipologia | Licenza | |
|---|---|---|---|---|
| 2017_Corli-diRuvo-Malaguti-Rosini_NHM.pdf | Full text editoriale | Full text (versione editoriale) | NON PUBBLICO - Accesso privato/ristretto | Administrator Richiedi una copia |
| 1701.08032.pdf | Pre print | Pre-print |  | Open Access Visualizza/Apri |
http://hdl.handle.net/11392/2379524
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