Yuxia Guo

Boundary Feedback Stabilization of Shallow Shells

We consider the stabilization of the shallow shell by boundary feedbacks where the model has a middle surface of any shape. First, we put the shallow shell model in a suitable semigroup scheme. The existence, the uniqueness, and the properties of solutions to the shallow shell are then treated by the semigroup approach and the regularity of elliptic boundary value problems. Finally, we establish the uniform energy decay rate for the shallow shell under some checkable geometric conditions on the middle surface.

Relationship of the morse index and the

We consider the second order strongly indefinite differential system with superlinearities. By using the approximation method of finite element, we show that bounds on solutions of the restriction functional onto finite dimensional subspace are equivalent to bounds on their relative Morse indices. The obtained results can be used to establish a Morse theory for strongly indefinite functionals with superlinearities.