Juncheng Wei

Localized Patterns in the Gierer Meinhardt Model on a Cycle Graph

Abstract. In this study, we provide a detailed analysis of the spike solutions and their stability for the Gierer–Meinhardt model on discrete lattices. We explore several phenomena that have no analogs in the continuum limit. For example in the discrete case, the system retains s...

A General Nonuniqueness Result for Yamabe-Type Problems for Conformally Variational Riemannian Invariants

Abstract Given a conformally variational scalar Riemannian invariant I , we identify a sufficient condition for a compact Riemannian manifold to admit finite regular coverings with many nonhomothetic conformal rescalings with I constant. We also identify a sufficient condition fo...