讲座主题：“Nonlinear Evolution in Transition Phenomena in the Presence of Linear Instability”

主 讲 人:  Prof. Jun Yu

           Department of Mathematics and Statistics

           College of Engineering and Mathematical Sciences

            University of Vermont

时　  间：6月19日　3：30—5：00pm（周一下午） 

地　  点：高等研究中心1221会议室

主办单位：清华大学周培源应用数学研究中心

Abstract:.  Through examples of transition phenomena in channel flow, solid combustion and geophysical fluid dynamics, this talk concerns the asymptotic behavior of small disturbances as they evolve in time in the presence of linear instability. The mathematical problem is rather interesting as solutions of the linearized equations are unstable when a parameter passes through a critical value. Thus, it is crucial to account for the cumulative effect of small nonlinearities to obtain a correct description of the evolution over long times. Weakly unstable problems where the parameter marginally crosses the neutral value are analyzed and the multiple scale expansions, as well as the Fourier method, are used to derive the dominant evolution equation. We present both asymptotic and numerical solutions and demonstrate transient behavior as well as the formation of coherent structures. Some recent new results in studying the Eady’s baroclinic instability model will also be discussed.

Dr. Jun Yu obtained his Ph.D from University of Washington, Seattle. He is now professor and associate chair in departments of mathematics & statistics,　University of Vermont. Dr. Yu is also professor of computer science　and affiliated faculty of mechanical engineering. The research areas of Dr. Yu include mathematical modeling, asymptotic and numerical analysis of differential equations, hydrodynamic stability, perturbation theory, biomedical mathematics.　shallow-water waves, human brain modeling, ocean and sea ice study, etc.

清华大学周培源应用数学研究中心

秘　书：　唐　琳

TEL：62797063