# American Institute of Mathematical Sciences

December  2013, 18(10): 2569-2596. doi: 10.3934/dcdsb.2013.18.2569

## Blow-up in finite or infinite time for quasilinear degenerate Keller-Segel systems of parabolic-parabolic type

 1 Department of Mathematics, Tokyo University of Science, 1-3 Kagurazaka, Shinjuku-ku, Tokyo 162-8601

Received  November 2012 Revised  July 2013 Published  October 2013

This paper gives a blow-up result for the quasilinear degenerate Keller-Segel systems of parabolic-parabolic type. It is known that the system has a global solvability in the case where $q < m + \frac{2}{N}$ ($m$ denotes the intensity of diffusion and $q$ denotes the nonlinearity) without any restriction on the size of initial data, and where $q \geq m + \frac{2}{N}$ and the initial data are small''. However, there is no result when $q \geq m + \frac{2}{N}$ and the initial data are large''. This paper discusses such case and shows that there exist blow-up energy solutions from initial data having large negative energy.
Citation: Sachiko Ishida, Tomomi Yokota. Blow-up in finite or infinite time for quasilinear degenerate Keller-Segel systems of parabolic-parabolic type. Discrete & Continuous Dynamical Systems - B, 2013, 18 (10) : 2569-2596. doi: 10.3934/dcdsb.2013.18.2569
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