Global Bifurcation from the Real Leading Eigenvalue of the Transport Operator. Issue 4 (7th June 2017) - Ammar, Aymen; Jeribi, Aref; Mahfoudhi, Kamel
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.