{
  "id": "2211.13571",
  "version": "v1",
  "published": "2022-11-24T12:43:50.000Z",
  "updated": "2022-11-24T12:43:50.000Z",
  "title": "Stress-modulated growth in the presence of nutrients -- existence and uniqueness in one spatial dimension",
  "authors": [
    "Kira Bangert",
    "Georg Dolzmann"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "Existence and uniqueness of solutions for a class of models for stress-modulated growth is proven in one spatial dimension. The model features the multiplicative decomposition of the deformation gradient $F$ into an elastic part $F_e$ and a growth-related part $G$. After the transformation due to the growth process, governed by $G$, an elastic deformation described by $F_e$ is applied in order to restore the Dirichlet boundary conditions and therefore the current configuration might be stressed with a stress tensor $S$. The growth of the material at each point in the reference configuration is given by an ordinary differential equation for which the right-hand side may depend on the stress $S$ and the pull-back of a nutrient concentration in the current configuration, leading to a coupled system of ordinary differential equations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-11-24T12:43:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "74L15",
      "92C10"
    ],
    "keywords": [
      "spatial dimension",
      "stress-modulated growth",
      "ordinary differential equation",
      "uniqueness",
      "current configuration"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}