Uniqueness and continuity of solution for the initial data in the scaling invariant class of the degenerate Keller-Segel system

Yoshie Sugiyama, Yumi Yahagi

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6 Citations (Scopus)

Abstract

We consider the degenerate Keller-Segel system (KS)m below. We find the functional space LS (0, T; Lp(ℝ)N)) with some p,s for the uniqueness and continuity of weak solutions with respect to the initial data. Our space is discussed from a viewpoint of the scaling invariant class associated with (KS)m for γ = 0. The technique is based on the L1-contraction principle for the porous medium equation.

Original languageEnglish
Pages (from-to)319-337
Number of pages19
JournalJournal of Evolution Equations
Volume11
Issue number2
DOIs
Publication statusPublished - Jun 1 2011

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All Science Journal Classification (ASJC) codes

  • Mathematics (miscellaneous)

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