Decay estimates for the biharmonic equation with applications to Saint-Venant principles in plane elasticity and Stokes flows

In a recent paper [1], J. K. Knowles has established new energy decay estimates for solutions of the biharmonic equation in a semi-infinite strip, subject to nonzero boundary conditions on the near end only. Such estimates, which predict an exponential decay of energy with axial distance from the end, have been used in the analysis of Saint-Venant's principle in plane elastostatics. (See [2] for a review of recent work on principles of Saint-Venant type; for a discussion of earlier results in the linear theory of elasticity, see These results are also relevant to the study of the spatial evolution of stationary Stokes flows in a semi-infinite parallel plate channel to fully-developed Poiseuille flow [4],