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| As to the power-type degenerate Keller-Segel system, we know that there is a possibly grow-up solution in the sub-critical case and that there is a bounded solution with the small initial data and an unbounded solution in finite or infinite time with the large negative energy initial data in the super-critical case. However, from research on the non-degenerate Keller-Segel system, we expect that the solution is bounded in the sub-critical case and moreover that the solution blows up in finite-time for the large negative energy initial data in the super-critical case. So, we'd like to discuss these themes in this talk. |
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