Possibility of the existence of blow-up solutions to quasilinear degenerate Keller-Segel systems of parabolic-parabolic type

摘要

This paper deals with the quasilinear 'degenerate' Keller-Segel system of parabolic-parabolic type under the super-critical condition. In the 'non-degenerate' case, Winkler (Math. Methods Appl. Sci. 2010; 33:12-24) constructed the initial data such that the solution blows up in either finite or infinite time. However, the blow-up under the super-critical condition is left as an open question in the 'degenerate' case. In this paper, we try to give an answer to the question under assuming the existence of local solutions.