期刊
JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES
卷 84, 期 9, 页码 1235-1260出版社
ELSEVIER
DOI: 10.1016/j.matpur.2005.04.001
关键词
relative entropy; fragmentation equations; cell division; self-similar solutions; periodic solutions; long time asymptotic
We introduce the notion of General Relative Entropy Inequality for several linear PDEs. This concept extends to equations that are not conservation laws, the notion of relative entropy for conservative parabolic, hyperbolic or integral equations. These are particularly natural in the context of biological applications where birth and death can be described by zeroth order terms. But the concept also has applications to more general growth models as the fragmentation equations. We give several types of applications of the General Relative Entropy Inequality: a priori estimates and existence of solution, long time asymptotic to a steady state, attraction to periodic solutions for periodic forcing. (c) 2005 Elsevier SAS. All rights reserved.
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