In this work we study a mathematical model which describes the antiplane shear deformation of a cylinder in frictionless contact with a rigid foundation. The material is assumed to be electro-viscoelastic with long-term memory, and the friction is modeled with Tresca's law and the foundation is assumed to be electrically conductive. First we derive the classical variational formulation of the model which is given by a system coupling an evolutionary variational equality for the displacement field and a time-dependent variational equation for the potential field. Then we prove the existence of a unique weak solution to the model. Moreover, the Proof is based on arguments of evolution equations and by using the Banach fixed-point theorem.

In the present paper, the SIR model tracks the numbers of susceptible, infected and recovered individuals during an epidemic with the help of ordinary differential equations (ODE). First, we give the model formulation of our phenomena. Secondly, a fully discrete difference scheme is derived for the SIR model.At the end of this aper, we give the simulation results of the model. A comparison of the obtained numerical results of both the models is performed in the absence of an exact solution.

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This paper deals with the study of a mathematical model which describes the bilateral, frictionless adhesive contact between two viscoelastic bodies with damage. The adhesion of the contact surfaces is considered and is modeled with a surface variable, the bonding field, whose evolution is described by a first order differential equation. We establish a variational formulation for the problem and prove the existence and uniqueness result of the solution. The proofs are based on time-dependent variational equalities, a classical existence and uniqueness result on parabolic equations, differential equations, and fixed-point arguments.

We study a mathematical model which describes the antiplane shear deformation of a cylinder in frictionless contact with a rigid foundation. The material is assumed to be electro-viscoelastic with long-term memory, the friction is modeled with Tresca's law and the foundation is assumed to be electrically conductive. First we derive the classical variational formulation of the model which is given by a system coupling an evolutionary variational equality for the displacement field, a time-dependent variational equation for the potential field and a differential equation for the bounding field. Then we prove the existence of a unique weak solution for the model. The proof is based on arguments of evolution equations and the Banach fixed point theorem.