# Eigenelements of a General Aggregation-Fragmentation Model - Mathematics > Analysis of PDEs

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Abstract: We consider a linear integro-differential equation which arises to describeboth aggregation-fragmentation processes and cell division. We prove theexistence of a solution $\lb,\U,\phi$ to the related eigenproblem. Sucheigenelements are useful to study the long time asymptotic behaviour ofsolutions as well as the steady states when the equation is coupled with anODE. 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 likeproteins aggregation. Non lower-bounded transport terms bring difficulties tofind $a\ priori$ estimates. All the work of this paper is to solve this problemusing weighted-norms.

Autor: Marie Doumic-Jauffret INRIA Rocquencourt, Pierre Gabriel LJLL

Fuente: https://arxiv.org/