一般聚集-破碎模型的特征元
Eigenelements of a General Aggregation-Fragmentation Model
摘要：
我们考虑一个线性积分微分方程，它描述了聚集-碎裂过程和细胞分裂。我们证明了相关特征值问题的解$(\lb,\U,ϕ)$的存在性。这些特征元对于研究方程与常微分方程耦合时解的长时间渐近性态以及定态是有用的。我们的研究涉及到一个非恒定的传输项，可以消失在$x=0,$，因为它似乎是相关的描述一些生物过程，如蛋白质聚集。非下界输运项给$a\ priori$估计带来困难。本文的全部工作就是利用加权范数来解决这一问题。
英文摘要：
We consider a linear integro-differential equation which arises to describe both aggregation-fragmentation processes and cell division. We prove the existence of a solution $(\lb,\U,ϕ)$ to the related eigenproblem. Such eigenelements are useful to study the long time asymptotic behaviour of solutions as well as the steady states when the equation is coupled with an ODE. Our study concerns a non-constant transport term that can vanish at $x=0,$ since it seems to be relevant to describe some biological processes like proteins aggregation. Non lower-bounded transport terms bring difficulties to find $a\ priori$ estimates. All the work of this paper is to solve this problem using weighted-norms.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
