{
  "id": "2303.01364",
  "version": "v2",
  "published": "2023-03-02T15:49:33.000Z",
  "updated": "2023-04-06T13:07:09.000Z",
  "title": "Convergence to self-similar profiles in reaction-diffusion systems",
  "authors": [
    "Alexander Mielke",
    "Stefanie Schindler"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We study a reaction-diffusion system on the real line, where the reactions of the species are given by one reversible reaction according to the mass-action law. We describe different positive limits at both sides of infinity and investigate the long-time behavior. Rescaling space and time according to the parabolic scaling, we show that solutions converge exponentially to a constant profile. In the original variables these profiles correspond to asymptotically self-similar behavior describing the diffusive mixing or equilibration of the different states at infinity. Our method provides global exponential convergence for all initial states with finite relative entropy.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2023-04-06T13:07:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35K57",
      "35C06",
      "35B45"
    ],
    "keywords": [
      "reaction-diffusion system",
      "self-similar profiles",
      "global exponential convergence",
      "long-time behavior",
      "finite relative entropy"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}