Global solvability of the regularized problem of growing hyperelastic materials

Abstract

We introduce a model of volumetric growth of biological materials which is based on the theory of finite elastic deformations. Surface effects at the boundary of the growing material are taken into account. Some newmathematical results for the model are obtained, and most significant among them is the existence of a global solution. The proof of this is presented in complete form. These results can be useful in further scientific developments at the confluence of biology and mechanics.