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Exact controllability for nonlinear thermoviscoelastic plate problem

Moulahi Taoufik, Aouadi Moncef, Althobaiti Saad

Demonstratio Mathematica

2024

Vol. 57, nr 1

art. no. 20240071

In this article, we consider a problem of exact controllability in the processes described by a nonlinear damped thermoviscoelastic plate. First, we prove the global well-posedness result for the nonlinear functions that are continuous with respect to time and globally Lipschitz with respect to space variable. Next, we perform a spectral analysis of the linear and uncontrolled problem. Then, we prove that the corresponding solutions decay exponentially to zero at a rate determined explicitly by the physical constants. Finally, we prove the exact controllability of the linear and the nonlinear problems by proving that the corresponding controllability mappings are surjective.