Istituto di Matematica Applicata e Tecnologie Informatiche     
Bonetti E., Schimperna G. Local Existence to Frémond's Model for Damaging in Elastic Materials. Preprint ercim.cnr.ian//2002-1303, 2002.
We consider a dissipative model recently proposed by M. Frémond and describing the evolution of damage in elastic materials. The corresponding PDE's system consists of an elliptic equation for the displacements with a degenerating elastic coefficient coupled with a variational dissipative inclusion governing the evolution of damage. We can prove a local in time existence result for an associated initial and boundary value problem, namely considering the evolution in some subinterval where the damage is not complete. The existence result is obtained by a truncation technique combined with suitable a priori estimates. Finally, we give an analogous local in time existence result in the case when the macroscopic equilibrium equation is of parabolic type, i.e., we introduce viscosity in the relation for macroscopic displacements.
Subject Damage, elastic materials, evolution system, variational formulation, dissipative inclusion
35R35, 74B10, 74R99

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