On an irreducibility type condition for the ergodicity of nonconservative semigroups
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Publication:6325413
DOI10.5802/CRMATH.92arXiv1909.07363MaRDI QIDQ6325413
Bertrand Cloez, Pierre Gabriel
Publication date: 16 September 2019
Abstract: We propose a simple criterion, inspired from the irreducible aperiodic Markov chains, to derive the exponential convergence of general positive semi-groups. When not checkable on the whole state space, it can be combined to the use of Lyapunov functions. It differs from the usual generalization of irreducibility and is based on the accessibility of the trajectories of the underlying dynamics. It allows to obtain new existence results of principal eigenelements, and their exponential attractiveness, for a nonlocal selection-mutation population dynamics model defined in a space-time varying environment.
Problems related to evolution (92D15) Asymptotic behavior of solutions to PDEs (35B40) One-parameter semigroups and linear evolution equations (47D06) Population dynamics (general) (92D25) Ergodic theory of linear operators (47A35) Branching processes (Galton-Watson, birth-and-death, etc.) (60J80)
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