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 |
---|---|
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