### Abstract

Weak solutions of the spatially inhomogeneous (diffusive) Aizenmann-Bak model of coagulation-breakup within a bounded domain with homogeneous Neumann boundary conditions are shown to converge, in the fast reaction limit, towards local equilibria determined by their mass. Moreover, this mass is the solution of a nonlinear diffusion equation whose nonlinearity depends on the (size-dependent) diffusion coefficient. Initial data are assumed to have integrable zero order moment and square integrable first order moment in size, and finite entropy. In contrast to our previous result [5], we are able to show the convergence without assuming uniform bounds from above and below on the number density of clusters. © Taylor & Francis Group, LLC.

Original language | English |
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Pages (from-to) | 1338-1351 |

Journal | Communications in Partial Differential Equations |

Volume | 34 |

DOIs | |

Publication status | Published - 1 Nov 2009 |

### Keywords

- Coagulation-breakup equation
- Duality arguments
- Entropy-based estimates
- Fast-reaction limit
- Nonlinear diffusion equations

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## Cite this

Carrillo, J. A., Desvillettes, L., & Fellner, K. (2009). Rigorous derivation of a nonlinear diffusion equation as fast-reaction limit of a continuous coagulation-fragmentation model with diffusion.

*Communications in Partial Differential Equations*,*34*, 1338-1351. https://doi.org/10.1080/03605300903225396