Code(s) de Classification MSC:
Code(s) de Classification CR:
Abstract : We consider a linear integro-differential equation which arises to describe both aggregation-fragmentation processes and cell division. We prove the existence of a solution (λ, U , φ) to the related eigenproblem, where λ denotes its first eigenvalue. Our study concerns a non-constant transport term that can vanish at x = 0. Non lower-bounded transport terms bring difficulties to find a priori estimates. We use weighted-norms to solve this problem.
Mots Clés: Aggregation-fragmentation equations, Eigenproblem, Size repartition, Polymerization process, cell division, Long-time asymptotic