{
  "id": "1905.03667",
  "version": "v1",
  "published": "2019-05-09T14:43:26.000Z",
  "updated": "2019-05-09T14:43:26.000Z",
  "title": "Stability of steady states and bifurcation to traveling waves in a free boundary model of cell motility",
  "authors": [
    "Leonid Berlyand",
    "Volodymyr Rybalko"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We introduce a two-dimensional Keller-Segel type free boundary model for motility of eukaryotic cells on substrates. The key ingredients of this model are the Darcy law for overdamped motion of the cytoskeleton (active) gel and Hele-Shaw type boundary conditions (Young-Laplace equation for pressure and continuity of velocities). We first show that radially symmetric steady state solutions become unstable and bifurcate to traveling wave solutions. Next we establish linear and nonlinear stability of the steady states. We show that linear stability analysis is inconclusive for both steady states and traveling waves. Therefore we use invariance properties to prove nonlinear stability of steady states.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-05-09T14:43:26.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "traveling wave",
      "cell motility",
      "symmetric steady state solutions",
      "keller-segel type free boundary model",
      "two-dimensional keller-segel type free boundary"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}