Exponential decay for the fragmentation or cell-division equation

By Benoit Perthame, Lenya Ryzhik. 2005

146 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Mechanics

View Paper: https://www.semanticscholar.org/paper/56421c9d5a36cabee370876b429e243f106e1b4d

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In Applied Mathematics

In Computational Mechanics

Citations in the corpus

A non‐conservative Harris ergodic theorem (2019, background): “Second, an explicit spectral gap was known only in the case of a constant division rate [11, 24, 68, 77, 83, 95].”
Exponential decay for the growth-fragmentation/cell-division equation (2009, background): “(9) Up to our knowledge it is not possible to obtain exponential decay with only control of Lp-norms on the initial data (even though we are not aware of an explicit counterexample).”
Limit theorems for some branching measure-valued processes (2011, methodology): “! In order to have the many-to-one formula, we give a condition for the existence of eigenelement extracted to [46] (see [45], for an asymmetric division cell, and [19], for a non linear motion between the division).”
Diffusive and nondiffusive population models (2010, background): “and the constant C > 0 depends on the initial datum u0. A similar result holds for nonconstant birth rates, see [ 122 ].”
Statistical estimation of a growth-fragmentation model observed on a genealogical tree (2012, methodology): “. A paradigmatic example, which can serve both as a toy model and a proof of concept for the methodology we develop here, is given by the growthfragmentation or size-structured cell division equation [33]. When applied to the evolution of a bacterial population it reads 8 < : @ tn(t;x) + ˝@ x xn(”
Spectral analysis of semigroups and growth-fragmentation equations (2013, methodology): “One can then show using the Brouwer-Tykonov Theorem that there exists a steady state f∞ by proceeding exactly as for the self-similar fragmentation equation [34, Section 3] (see also [94, 68] where other arguments are presented).”
Eigenelements of a General Aggregation-Fragmentation Model (2009, background): “Following an idea introduced in [32] we notice that the equation in (19) satisfied by φη is a transport equation and therefore satisfies the maximum principle (see Lemma 4 in the Appendix).”
General entropy equations for structured population models and scattering (2004, background): “(ii) (Size structured) This is known for b(x) constant and small perturbation of constants (see [18,16]) nonlinear related models have been treated (s e [10] and the references therein).”
General relative entropy inequality: an illustration on growth models (2005, methodology): “We refer to [ 26 , 23] for the idea developed here, and we only sketch the main estimates.”
Rate of convergence to an asymptotic profile for the self-similar fragmentation and growth-fragmentation equations (2010, background): “The literature on concrete applications is quite large and we refer the reader to [7, 12] as general sources on the topic, and to the references cited in [3, 8, 13] for particular applications.”