Doctoral Dissertations

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Global existence and exponential stability for some dynamic contact problems
(University of M'Sila, 2024-06-27) Imane Ouakil
In this thesis, we study some dynamic contact problems, with or without friction, between a deformable body and a foundation. We consider a nonlinear constitutive law with long memory term for viscoelastic or thermo-viscoelastic materials. The acceleration of the system is not neglected and then the modeled processes are dynamic. The contact is modeled with different conditions including normal compliance, normal damped response and normal compliance with adhesion. Moreover, the considered contact is bilateral because it is maintained at any time. The results we obtain concern the global existence and uniqueness of mild solutions. The techniques that we used are based on the theory of operators, fixed point and a nonlinear semigroup arguments. We also aim to establish the exponential stability of the obtained solutions using energy method and under some assumptions on problem data.