Global Bifurcation from the Real Leading Eigenvalue of the Transport Operator. Issue 4 (7th June 2017)

• Record Type: Journal Article
• Authors: Ammar, Aymen; Jeribi, Aref; Mahfoudhi, Kamel
• Is Part Of: Journal of computational and theoretical transport. Volume 46:Issue 4(2017)
• Page Start: 229
• Page End: 241
• Publication Date: 2017-06-07
• Subjects: Global bifurcations -- leading eigenvalue -- transport operator; Transport theory -- Periodicals; Statistical physics -- Periodicals; Statistical physics; Transport theory; Periodicals; 530.138
• DOI: 10.1080/23324309.2017.1336729
• Languages: English
• ISSNs: 2332-4309

Abstract

ABSTRACT: The present paper deals with a nonlinear transport equation derived from a model introduced by Rotenberg ( J. Theor. Biol., vol. 103, 1983, pp. 181–199), which describes the growth of a cell population. Each cell of this population is distinguished by its degree of maturation x and its maturation velocity y . We discussed some bifurcation results for a class of nonlinear transport operators under vacuum boundary conditions. Our results are based on the classical global bifurcation theorem of Rabinowitz type. Finally, some open problems are indicated.