A Carleman type estimate for the Mindlin-Timoshenko plate model

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Kurz, Jason A.
Carleman; estimate; Mindlin; plate; Timoshenko
thesis / dissertation description
This thesis focuses on results concerning providing a Carleman type estimate for the Mindlin-Timoshenko plate equations. The main approach is to provide an estimate for each of the three equations in the model then present these estimates in totality as a singular Carleman estimate for the entire model. The initial equation in the model is a simple two dimensional hyperbolic partial differential equation known as the wave equation. Prior research has been done for this type of equation and will be applied to provide the Carleman estimate for the first equation in the model. The estimate for the second and third equations will be derived by first establishing a point-wise inequality for the principal part of the equation multiplied by an exponential weight. After establishing a suitable pseudo-convex function for the exponential weight factor, specifications will be applied to the established point-wise estimates which will lead to the Carleman type estimates and their corresponding integral inequalities.