Existence of self-similar solutions to a parabolic system modelling chemotaxis

  • Naomi Muramoto
  • Yūki Naito
  • Kiyoshi Yoshida


We investigate a semilinear elliptic equation
with a parameter λ > 0 and a constant 0 < ε < 2, and obtain a structure of the pair (λ, υ) of a parameter and a solution which decays at infinity. This equation arises in the study of self-similar solutions for the Keller-Segel system. Our main results are as follows: (i) There exists a λ* > 0 such that if 0 < λ < λ*, (SE) has two distinct solutionsυ λ and guλ satisfyingυ λ < guλ, and that if λ > λ*, (SE) has no solution, (ii) If λ = λ* and 0 < ε < 1, (SE) has the unique solution υ*; (iii) The solutionsυ λ and υλ are connected through υ*.

Key words

self-similar solution chemotaxis elliptic equation global branch 


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Copyright information

© JJIAM Publishing Committee 2000

Authors and Affiliations

  • Naomi Muramoto
    • 1
  • Yūki Naito
    • 2
  • Kiyoshi Yoshida
    • 3
  1. 1.Department of Mathematics, Faculty of ScienceHiroshima UniversityHigashi-HiroshimaJapan
  2. 2.Department of Applied Mathematics, Faculty of EngineeringKobe UniversityKobeJapan
  3. 3.Division of Mathematical and Information Sciences, Faculty of Integrated Arts and SciencesHiroshima UniversityHigashi-HiroshimaJapan

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