Exponential decay for the fragmentation or cell-division equation |
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Authors: | Benoî t Perthame,Lenya Ryzhik |
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Affiliation: | a Département de Mathématiques et Applications, École Normale Supérieure, CNRS UMR8553, 45 rue d’Ulm, F 75230 Paris Cedex 05, France b Department of Mathematics, University of Chicago, Chicago IL 60637, USA |
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Abstract: | We consider a classical integro-differential equation that arises in various applications as a model for cell-division or fragmentation. In biology, it describes the evolution of the density of cells that grow and divide. We prove the existence of a stable steady distribution (first positive eigenvector) under general assumptions in the variable coefficients case. We also prove the exponential convergence, for large times, of solutions toward such a steady state. |
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Keywords: | Cell division Fragmentation Asymptotic stability |
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