Self-similarity in a General Aggregation-Fragmentation Problem ; Application to Fitness Analysis

Abstract

We consider the linear growth and fragmentation equation with general coefficients. Under suitable conditions, the first eigenvalue represents the asymptotic growth rate of solutions, also called \emph{fitness} or \emph{Malthus coefficient} in population dynamics ; it is of crucial importance to understand the long-time behaviour of the population. We investigate the dependency of the dominant eigenvalue and the corresponding eigenvector on the transport and fragmentation coefficients. We show how it behaves asymptotically as transport dominates fragmentation or \emph{vice versa}. For this purpose we perform suitable blow-up analysis of the eigenvalue problem in the limit of small/large growth coefficient (resp. fragmentation coefficient). We exhibit possible non-monotonic dependency on the parameters, conversely to what would have been conjectured on the basis of some simple cases.

References in corpus (6)

• On the Inverse Problem for a Size-Structured Population Model
• Rate of convergence to an asymptotic profile for the self-similar fragmentation and growth-fragmentation equations
• An inequality for the Perron and Floquet eigenvalues of monotone differential systems and age structured equations
• Long-time Asymptotics for Nonlinear Growth-fragmentation Equations
• The Shape of the Polymerization Rate in the Prion Equation
• High-order WENO scheme for Polymerization-type equations

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