On the exponential decay of the energy of a linear thermoelastic plate
The linear plate equations in a bounded domain in \(\mathbb{R}^ n\), \(u_{tt} + \Delta^ 2 u + \alpha \Delta \theta = 0\), \(\theta_ t - \beta \Delta \theta - \alpha \Delta u_ t = 0\), \(\beta, | \alpha| > 0\), are studied with prescribed initial conditions and with the following Neumann type boundary conditions: the function \(v = \Delta u + \alpha \theta\) as well as the normal derivatives of \(v\) and of \(\theta\) vanish on the boundary. For this mathematically interesting problem it is shown the well-posedness along with semigroup theory, and the exponential decay using energy methods.
scientific article; zbMATH DE number 704198