Asymptotic behavior of solutions to plate equations with nonlinear dissipation occurring through shear forces and bending moments

We consider the question of strong stability of solutions to plate equations with nonlinear dissipation in the boundary conditions. Two cases are discussed: (1) dissipation occurring through the nonlinear forces applied on the boundary and (2) dissipation acting through the nonlinear moments. Asymptotic stability results are presented for both cases. In the first case the results are established under the natural geometric conditions imposed on the domain, while in the second case certain restrictions on the curvature on the active portion of the boundary are required.Research partially supported by NSF Grant DMS-8301668 and by AFOSR Grant AFOSR-84-0365.