Motivated by experimental studies on the anomalous diffusion of biological populations, we study the spectral square root of the Laplacian in bounded domains with Neumann homogeneous boundary conditions. Such operator arises in the continuous limit for long jumps random walks with reflecting barriers. Existence and uniqueness results for positive solutions are proved in the case of indefinite nonlinearities of logistic type by means of bifurcation theory.

Fractional diffusion with Neumann boundary conditions: The logistic equation / Montefusco, Eugenio; Benedetta, Pellacci; Gianmaria, Verzini. - In: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. SERIES B.. - ISSN 1531-3492. - STAMPA. - 18:8(2013), pp. 2175-2202. [10.3934/dcdsb.2013.18.2175]

Fractional diffusion with Neumann boundary conditions: The logistic equation

MONTEFUSCO, Eugenio;
2013

Abstract

Motivated by experimental studies on the anomalous diffusion of biological populations, we study the spectral square root of the Laplacian in bounded domains with Neumann homogeneous boundary conditions. Such operator arises in the continuous limit for long jumps random walks with reflecting barriers. Existence and uniqueness results for positive solutions are proved in the case of indefinite nonlinearities of logistic type by means of bifurcation theory.
2013
bifurcation theory; spectral fractional laplacian; eigenvalue problems for nonlocal operators
01 Pubblicazione su rivista::01a Articolo in rivista
Fractional diffusion with Neumann boundary conditions: The logistic equation / Montefusco, Eugenio; Benedetta, Pellacci; Gianmaria, Verzini. - In: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. SERIES B.. - ISSN 1531-3492. - STAMPA. - 18:8(2013), pp. 2175-2202. [10.3934/dcdsb.2013.18.2175]
File allegati a questo prodotto
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/518550
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 44
  • ???jsp.display-item.citation.isi??? 45
social impact