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CATEGORIES:Part III Seminars
SUMMARY:Lewy's Example - Conor Heffernan
DTSTART;TZID=Europe/London:20180315T153000
DTEND;TZID=Europe/London:20180315T163000
UID:TALK103036AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/103036
DESCRIPTION:During ‘Analysis of PDEs’ in Michaelmas term we pr
oved the Cauchy-Kovalevskaya theorem. The theorem
asserts the local existence of a solution for a ce
rtain class of first order systems of PDEs. The hy
pothesis of the theorem requires all given functio
ns within the system are analytic. The analyticict
y is a key component of the hypothesis as the cele
brated example due to Lewy shows that smoothness i
s not enough to guarantee these systems have solut
ions. This is done by construction of a linear PDE
which has no solutions at all. In this talk\, a s
tatement of the Cauchy-Kovalevskaya theorem will b
e given and the statement of Lewy’s example and a
proof (or at least a sketch\, depending on time) t
hat the example is in fact a PDE with no solutions
will also be given.
LOCATION:MR11
CONTACT:Kasia Wyczesany
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