Uniqueness and regularity of weak solutions for the 1-D degenerate KellerSegel systems

Yoshie Sugiyama

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)2230-2244
Number of pages15
JournalNonlinear Analysis, Theory, Methods and Applications
Volume73
Issue number7
DOIs
Publication statusPublished - Oct 1 2010
Externally publishedYes

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Weak Solution
Uniqueness
Regularity
Uniform Boundedness
Strong Solution
Imply
Estimate

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

Cite this

Uniqueness and regularity of weak solutions for the 1-D degenerate KellerSegel systems. / Sugiyama, Yoshie.

In: Nonlinear Analysis, Theory, Methods and Applications, Vol. 73, No. 7, 01.10.2010, p. 2230-2244.

Research output: Contribution to journalArticle

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