General entropy equations for structured population models and scattering

作者：Philippe Michel, Stéphane Mischler, Benoı̂t Perthame · 发表于：Comptes Rendus Mathématique · 年份：2004 · DOI：10.1016/j.crma.2004.03.006 · 被引用次数：75 · 研究领域：Gas Dynamics and Kinetic Theory、Advanced Thermodynamics and Statistical Mechanics、Mathematical Biology Tumor Growth

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.