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CATEGORIES:Geometric Analysis and Partial Differential Equati
ons seminar
SUMMARY:Nonlinear PDEs of Mixed Elliptic-Hyperbolic Type:
Analysis and Applications - Gui-Qiang Chen (Unive
rsity of Oxford)
DTSTART;TZID=Europe/London:20190610T150000
DTEND;TZID=Europe/London:20190610T160000
UID:TALK124615AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/124615
DESCRIPTION:As is well-known\, two of the basic types of linea
r partial differential equations (PDEs) are ellipt
ic and hyperbolic\, following the classification f
or linear PDEs proposed by Jacques Hadamard in the
1920s\; and linear theories of PDEs of these two
types have been relatively well developed. On the
other hand\, many nonlinear PDEs arising in geomet
ry\, mechanics\, and other areas naturally are of
mixed elliptic-hyperbolic type. The solution of so
me longstanding fundamental problems in these area
s greatly requires a deep understanding of such no
nlinear PDEs of mixed type. Important examples inc
lude shock reflection-diffraction problems in flui
d mechanics (the Euler equations) and isometric em
bedding problems in differential geometry and mate
rials science (the Gauss-Codazzi-Ricci equations)\
, among many others. In this talk we will present
natural connections of nonlinear PDEs of mixed ell
iptic-hyperbolic type with these longstanding prob
lems and will then discuss some recent development
s in the analysis of these nonlinear PDEs through
the examples with emphasis on developing and ident
ifying 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
CONTACT:Ivan Moyano
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