FINE ASYMPTOTICS OF PROFILES AND RELAXATION TO EQUILIBRIUM FOR GROWTH-FRAGMENTATION EQUATIONS WITH VARIABLE DRIFT RATES
FINE ASYMPTOTICS OF PROFILES AND RELAXATION TO EQUILIBRIUM FOR GROWTH-FRAGMENTATION EQUATIONS WITH VARIABLE DRIFT RATES
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DOI：
10.3934/krm.2013.6.219
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发表时间：
2013-06-01
影响因子：
1
通讯作者：
Gabriel, Pierre
中科院分区：
文献类型：
--
作者：
Balague, Daniel;Canizo, Jose A.;Gabriel, Pierre
我们关心的是增长-碎裂方程的长时间行为。我们证明精细估计的增长破碎运营商的主要本征函数，给他们的一阶行为接近0和+无穷大。使用这些估计，我们证明了一个谱间隙的结果，按照[1]中的技术，这意味着解决方案衰减到平衡指数快速。我们考虑的增长和分裂系数是相当普遍的，基本上只是假设行为渐近像幂律。
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.