We consider the KellerSegel system of degenerate type (KS)m with m>1 below. We prove the uniqueness of weak solutions of (KS)m with the regularity of ∂tu∈Lloc 1(ℝ×(0,T)). In addition, we shall show that every weak solution of (KS)m has the property that ∂tu belongs to L locp(ℝ×(0,T)) for all p∈[1,m+1/m). This implies that the weak solution u actually becomes a strong solution. These results are obtained as applications of the Aronson-Bénilan type estimate to (KS)m, i.e., there is a uniform boundedness from below of ∂χ2um-1.
|Number of pages||15|
|Journal||Nonlinear Analysis, Theory, Methods and Applications|
|Publication status||Published - Oct 1 2010|
All Science Journal Classification (ASJC) codes
- Applied Mathematics