| Abstract: |
| Keller-Segel type cross-diffusion systems have been playing an
outstanding role in the understanding of various patterning phenomena in
biology. Concentrating on issues of predominant application relevance,
the description of taxis-driven explosions has been among the most
challenging topics in their analysis, and a natural focus of the
literature in this regard is on the characterization of solution
behavior near collapse. The presentation aims at reporting both on
classical and on some recent developments, with a particular focus on
the identification of circumstances under which solutions either must
blow up at single points only, or alternatively may form singularities
throughout larger regions in space. |
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