Exact controllability for nonlinear thermoviscoelastic plate problem

Abstract

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.

Keywords

• nonlinear thermoviscoelastic plate
• spectral analysis
• optimal decay rate
• exact controllability
• 34d20
• 93b05
• 81q10