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SUMMARY:Nonlinear PDEs of Mixed Elliptic-Hyperbolic Type:  Analysis and Ap
 plications - Gui-Qiang Chen (University of Oxford)
DTSTART:20190610T140000Z
DTEND:20190610T150000Z
UID:TALK124615@talks.cam.ac.uk
CONTACT:Ivan Moyano
DESCRIPTION:As is well-known\, two of the basic types of linear partial di
 fferential equations (PDEs) are elliptic and hyperbolic\, following the cl
 assification for linear PDEs proposed by Jacques Hadamard in the 1920s\; a
 nd linear theories of PDEs of these two types have been relatively well de
 veloped. On the other hand\, many nonlinear PDEs arising in geometry\, mec
 hanics\, and other areas naturally are of mixed elliptic-hyperbolic type. 
 The solution of some longstanding fundamental problems in these areas grea
 tly requires a deep understanding of such nonlinear PDEs of mixed type. Im
 portant examples include shock reflection-diffraction problems in fluid me
 chanics (the Euler equations) and isometric embedding problems in differen
 tial geometry and materials science (the Gauss-Codazzi-Ricci equations)\, 
 among many others. In this talk we will present natural connections of non
 linear PDEs of mixed elliptic-hyperbolic type with these longstanding prob
 lems and will then discuss some recent developments in the analysis of the
 se nonlinear PDEs through the examples with emphasis on developing and ide
 ntifying unified approaches\, ideas\, and techniques for dealing with the 
 mixed-type problems. Further trends\, perspectives\, and open problems in 
 this direction will also be addressed.
LOCATION:CMS\, MR13
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