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Traveling waves of a full parabolic attraction-repulsion chemotaxis system with logistic source

Rachidi B. Salako

Published 2019 in Discrete and Continuous Dynamical Systems. Series A

ABSTRACT

. In this paper, we study traveling wave solutions of the chemotaxis system where τ > 0 ,χ i > 0 ,λ i > 0 , µ i > 0 ( i = 1 , 2) and a > 0 , b > 0 are constants. Under some appropriate conditions on the parameters, we show that there exist two positive constant c ∗ ( τ,χ 1 ,µ 1 1 2 2 2 ) such that for every c ∗ ( τ,χ 1 ,µ 1 ,λ 1 ,χ 2 ,µ 2 ,λ ≤ λ 2 ), has a traveling wave solution ( u,v 1 ,v 2 )( x,t U,V ct ) connecting ( ab , aµ , aµ 2 bλ 2 ) and (0 , 0 , 0) satisfying where µ ∈ (0 , √ a ) is such that c = c µ := µ + aµ . Moreover, ,λ 1 ,χ 2 ,µ 2 ,λ 2 ) = ∞ and lim ( χ 1 ,χ 2 ) → (0 + , 0 + )) c ∗ ( τ,χ 1 ,µ 1 ,λ 1 ,χ 2 ,µ 2 ,λ 2 ) = c ˜ µ ∗ , where ˜ µ ∗ = min {√ a, (cid:113) λ 1 + τa (1 − τ ) + , (cid:113) λ 2 + τa (1 − τ ) + } . We also show that (0.1) has no traveling wave solution connecting ( a b , aµ 1 bλ 1 , aµ 2 bλ 2 ) and (0 , 0 , 0) with speed c < 2 √ a .

PUBLICATION RECORD

  • Publication year

    2019

  • Venue

    Discrete and Continuous Dynamical Systems. Series A

  • Publication date

    Unknown publication date

  • Fields of study

    Not labeled

  • Identifiers
    DOI 10.3934/dcds.2019260
  • External record

    Open on Semantic Scholar

  • Source metadata

    Semantic Scholar

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