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Development of traveling waves in an interacting two-species chemotaxis model

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  • By constructing sub and super solutions, we establish the existence of traveling wave solutions to a two-species chemotaxis model, which describes two interacting species chemotactically reacting to a chemical signal that is degraded by the two species. We identify the full parameter regime in which the traveling wave solutions exist, derive the asymptotical decay rates of traveling wave solutions at far field and show that the traveling wave solutions are convergent as the chemical diffusion coefficient goes to zero.
    Mathematics Subject Classification: Primary: 35C07, 35K55, 46N60; Secondary: 62P10, 92C17.


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