Global existence and exponential stability for some dynamic contact problems
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Date
2024-06-27
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University of M'Sila
Abstract
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.
Description
Keywords
Asymptotic behavior, Contact problem, Dissipative, Global existence, Semigroup.