Advanced results on variational inequality formulation in oligopolistic market equilibrium problem

The aim of the paper is to study the regularity of the solution to the evolutionary variational inequality governing the dynamic oligopolistic market equilibrium problem in presence of production excesses. More precisely, we obtain a Lipschitz continuity result with respect to time for such a solution. Moreover, we introduce a discretization procedure for computing dynamic equilibrium solutions and we provide a numerical example.

AN ANTIPLANE CONTACT PROBLEM FOR VISCOELASTIC MATERIALS WITH LONG‐TERM MEMORY

We study a mechanical problem modeling the antiplane shear deformation of a cylinder in frictional contact with a rigid foundation. The material is assumed to be viscoelastic with long‐term memory, the process is quasistatic, and the friction is modeled with Tresca's law. The problem leads to an evolutionary variational inequality that we study in an abstract framework. We then use the abstract result to prove the existence of a unique weak solution to the mechanical model. Moreover, we study its behavior with respect to the memory term and establish a convergence result.