| Abstract: |
| The Keller-Rubinow model for Liesegang rings reduces to a single scalar reaction-diffusion equation in the fast-reaction limit, albeit with a non-local non-Lipshitz reaction term. In this talk, we present evidence that the pattern of successive precipitation regions and precipitation-free interrings breaks down in finite time, either by rings accumulating at finite locus or by degeneration of the ignition condition. We discuss the question of continuation after breakdown, time-asymptotic profile, and interpretation of the solution after breakdown as a precipitation probability density function. Finally, we discuss uniqueness of solutions and possibly scenarios for non-uniqueness. |
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