A nonlinear problem associated to the motion of a membrane (Q5945982)

Nonlinear motion of a membrane, described by the equation \(u_{tt}-\triangle u+\nabla \cdot b(\nabla u)=f,\) where \(b(z)=\rho ^2\frac{z}{\sqrt{1+|z|^2}},\) is approximated by a higher order equation adding the term \(\epsilon \triangle u_{tt}\) to the above equation. If weak solutions of the problem to the approximating equations and Dirichlet boundary conditions are ``physically significant'' (angular velocities are bounded), then their limit is a ``physically significant'' weak solution of the above equation. Moreover, uniqueness of such a solution is proved.