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EnglishThis paper develops the notion and properties of the generalized principal eigenvalue for an elliptic system coupling an equation in a plane with one on a line in this plane, together with boundary conditions that express exchanges taking place between the plane and the line. This study is motivated by the reaction-diffusion model introduced by Berestycki, Roquejoffre and Rossi [The influence of a line with fast diffusion on Fisher-KPP propagation, J. Math. Biol. 66(4-5) (2013) 743-766] to describe the effect on biological invasions of networks with fast diffusion imbedded in a field. Here we study the eigenvalue associated with heterogeneous generalizations of this model. In a forthcoming work [Influence of a line with fast diffusion on an ecological niche, preprint (2018)] we show that persistence or extinction of the associated nonlinear evolution equation is fully accounted for by this generalized eigenvalue. A key element in the proofs is a new Harnack inequality that we establish for these systems and which is of independent interest.
Generalized principal eigenvalues for heterogeneous road-field systems / Berestycki, H.; Ducasse, R.; Rossi, L.. - In: COMMUNICATIONS IN CONTEMPORARY MATHEMATICS. - ISSN 0219-1997. - 22:1(2020).
| Titolo: | Generalized principal eigenvalues for heterogeneous road-field systems | |
| Autori: | ROSSI, LUCA (Corresponding author) | |
| Data di pubblicazione: | 2020 | |
| Rivista: | ||
| Citazione: | Generalized principal eigenvalues for heterogeneous road-field systems / Berestycki, H.; Ducasse, R.; Rossi, L.. - In: COMMUNICATIONS IN CONTEMPORARY MATHEMATICS. - ISSN 0219-1997. - 22:1(2020). | |
| Handle: | http://hdl.handle.net/11573/1456700 | |
| Appartiene alla tipologia: | 01a Articolo in rivista |
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