Eigenelements of a General Aggregation-Fragmentation Model Doumic-Jauffret, Marie; Gabriel, Pierre

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Doumic-Jauffret, Marie ; Gabriel, Pierre
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Mathematical Models and Methods in Applied Sciences
mathematics - analysis of pdes; Models; aggregation-fragmentation equations
To access, purchase, authenticate, or subscribe to the full-text of this article, please visit this link: http://dx.doi.org/10.1142/S021820251000443X Byline: MARIE DOUMIC JAUFFRET, PIERRE GABRIEL 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 ([lamda], $\mathcal U$, I) to the related eigenproblem. Such eigenelements are useful to study the long-time asymptotic behavior 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.
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