FINE ASYMPTOTICS OF PROFILES AND RELAXATION TO EQUILIBRIUM FOR GROWTH-FRAGMENTATION EQUATIONS WITH VARIABLE DRIFT RATES

被引：26

作者：

Balague, Daniel ^{[1
]}

Canizo, Jose A. ^{[2
]}

Gabriel, Pierre ^{[3
]}

机构：

[1] Univ Autonoma Barcelona, Dept Matemat, Bellaterra 08193, Spain

[2] Univ Birmingham, Sch Math, Birmingham B15 2TT, W Midlands, England

[3] Univ Versailles St Quentin En Yvelines, Lab Math Versailles, CNRS UMR 8100, F-78035 Versailles, France

来源：

关键词：

Fragmentation; growth; eigenvalue problem; entropy; exponential convergence; long-time behavior; EXPONENTIAL DECAY;

D O I：

10.3934/krm.2013.6.219

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We are concerned with the long-time behavior of the growth-fragmentation equation. We prove fine estimates on the principal eigenfunctions of the growth-fragmentation operator, giving their first-order behavior close to 0 and +infinity. Using these estimates we prove a spectral gap result by following the technique in [1], which implies that solutions decay to the equilibrium exponentially fast. The growth and fragmentation coefficients we consider are quite general, essentially only assumed to behave asymptotically like power laws.

引用

页码：219 / 243

页数：25

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