{
  "id": "2010.11335",
  "version": "v1",
  "published": "2020-10-21T22:15:06.000Z",
  "updated": "2020-10-21T22:15:06.000Z",
  "title": "Traveling wave solutions for two species competitive chemotaxis systems",
  "authors": [
    "T. B. Issa",
    "R. B Salako",
    "W. Shen"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper, we consider two species chemotaxis systems with Lotka-Volterra competition reaction terms. Under appropriate conditions on the parameters in such a system, we establish the existence of traveling wave solutions of the system connecting two spatially homogeneous equilibrium solutions with wave speed greater than some critical number c*. We also show the non-existence of such traveling waves with speed less than some critical number c*_0, which is independent of the chemotaxis. Moreover, under suitable hypotheses on the coefficients of the reaction terms, we obtain explicit range for the chemotaxis sensitivity coefficients ensuring c*= c*_0, which implies that the minimum wave speed exists and is not affected by the chemoattractant.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-10-21T22:15:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B35",
      "35B40",
      "35K57",
      "35Q92",
      "92C17"
    ],
    "keywords": [
      "species competitive chemotaxis systems",
      "traveling wave solutions",
      "lotka-volterra competition reaction terms",
      "chemotaxis sensitivity coefficients",
      "species chemotaxis systems"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}