Existence and uniqueness of solution to an adaptive elasticity model

Jerome Monnier (1) , Luís Trabucho (2)

1 LMC - IMAG - Laboratoire de Modélisation et Calcul
2 CMAF - Centro de Matemática e Aplicações Fundamentais

In this work we study the existence and unicity of solutions to an {\sl Adaptive Elasticity Model} applied to bone remodeling. Specifically, we consider the model derived by Cowin and Hegedus, directly from continuum mechanics theory. We use a fixed point argument in order to prove the existence of solutions and a straightforward adaptation of the Cowin and Nachlinger analysis in order to prove uniqueness.

Domaines: Equations aux dérivées partielles [math.AP]; Biomécanique [physics.med-ph]; Biomécanique [physics.med-ph]

Jerome Monnier, Luís Trabucho. Existence and uniqueness of solution to an adaptive elasticity model. Mathematics and Mechanics of Solids, 1998, 3 (2), pp.217-228. ⟨10.1177/108128659800300206⟩. ⟨hal-00908283⟩