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arxiv 2504.05428 v1 pith:22EPUZHV submitted 2025-04-07 math.AP math.FA

Well-posedness and large time behavior of a size-structured growth-coagulation-fragmentation model

Saroj Si , Ankik Kumar Giri This is my paper
classification math.AP math.FA
keywords existenceweakbehaviorgrowth-coagulation-fragmentationlargeresultsize-structuredsolutions
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The existence and uniqueness of weak solutions to a size-structured growth-coagulation-fragmentation (GCF) equation with a renewal boundary condition are shown for a class of unbounded coagulation and fragmentation kernels. The existence proof is based on a weak compactness framework in the weighted $L^1$-space. This result extends the existence results of Banasiak and Lamb [14] and Ackleh et al. [2,4]. Furthermore, we establish a stability result and derive uniqueness as a direct consequence of it. Moreover, this study explores the large time behavior of weak solutions.

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