Exponential Decay Of Thermoelastic Plates With Dynamical Boundary Conditions

This thesis focuses on thermoelastic plates and thermoelastic transmission plates with damping and dynamical boundary conditions problem and we proved the expo-nential decay of solutions. The thesis is composed of three chapters, the main contents as follows:In chapter 1, we first introduce some terminologies and notations to partial differ-ential equations and semigroup of linear operators. Secondly, we introduce some theory and formulation to partial differential equations and semigroup of linear operators.In chapter 2, we first give a thermoelastic plates with damping and dynamical boundary conditions. This is a system composed of a thermoelastic plate equation with damping and ordinary differential equation, which is described as follows: Secondly, we can write the above system as an abstract system, then give the result that the corresponding Co-semigroup is exponential stabilization. Thirdly, by using the frequency domain criterion for exponential stability of Co-semigroup in Hilbert space, we prove that the Co-semigroup corresponding the thermoelastic system is exponential stabilization.In chapter 3,we first give a thermoelastic transmission plates with damping and dynamical boundary conditions. This is a system composed of a thermoelastic plates equation with damping and ordinary differential equation, which is described as fol- lows: Secondly, we can write the above system as an abstract system, then give the result that the corresponding Co-semigroup is exponential stabilization. Thirdly, by using the frequency domain criterion for exponential stability of Co-semigroup in Hilbert space, we prove that the Co-semigroup corresponding the thermoelastic system is exponential stabilization.