General entropy equations for structured population models and scattering

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Abstract

We consider several structured population models (age structured, size structured, maturity structured) and the general scattering equation. These models are not conservation laws, nevertheless, we show that they admit a common relative entropy structure which uses the first eigenelements of the problem. In case of scattering, it is more general than the usual 'detailed balance principle'. Three types of consequences are deduced from this entropy structure: a priori bounds, large time convergence to the steady state and in some cases, exponential rates of convergence. © 2004 Académie des sciences. Published by Elsevier SAS. All rights reserved.

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Michel, P., Mischler, S., & Perthame, B. (2004). General entropy equations for structured population models and scattering. Comptes Rendus Mathematique, 338(9), 697–702. https://doi.org/10.1016/j.crma.2004.03.006

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