UTA Department of Mathematics

Applied Mathematics Seminar

Date/Time/Room: Tuesday (7/30/2002) at 2:00pm in 304 Pickard Hall

Speaker: Weishi Liu, Department of Mathematics, University of Kansas

``A Geometric Theory for Singularly Perturbed Systems with Some Turning Points''

Abstract: In this talk, I will discuss a geometric theory for singularly perturbed systems with a certain type of turning points. We will examine the existence of invariant manifolds and establish several exchange lemmas. The purpose of exchange lemmas is to describe how the smooth configuration of an invariant manifold evolves as it passes the vicinity of the slow manifold, which is evidently the most important aspect of the global dynamics. As an application, we will identity a class of Riemann solutions of hyperbolic systems of conservation laws in one-space dimension and show that they are admissible in the sense of viscous wave fan profile criterion.