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Regularity Properties of Solutions of a Model for Morphoelastic Growth in the Presence of Nutrients in One Spatial Dimension
Julian Blawid, Georg Dolzmann
https://arxiv.org/abs/2507.22582

Regularity Properties of Solutions of a Model for Morphoelastic Growth in the Presence of Nutrients in One Spatial Dimension
Regularity properties of solutions for a class of quasi-stationary models in one spatial dimension for stress-modulated growth in the presence of a nutrient field are proven. At a given point in time the configuration of a body after pure growth is determined by means of a family of ordinary differential equations in every point in space. Subsequently, an elastic deformation, which is given by the minimizer of a hyperelastic variational integral, is applied in order to restore Dirichlet boundar…