| Abstract: |
| We present a global existence theory for weak solutions to a two-species cross-diffusion system, in one space dimension, in which the evolution of each species is governed by two mechanisms: a diffusion which acts only on the sum of the species with a logarithmic or fast diffusion type pressure law, and a drift term, which can differ between the two species. We will discuss two types of phenomena, regarding qualitative properties of solutions. First, we will show that if the initial densities are `totally mixed`, this property will propagate over time. Second, we will show how to remove the this condition on the initial data, resulting in weak solutions which can be only partially mixed. All these solutions are in contrast with the segregated solutions, known previously in the literature. The talk will be based on joint works with Guy Parker (Durham). |
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