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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Symmetries of Boundary Value Problems: Definitions
\, Algorithms and Applications to Physically Motiv
ated Problems - Cherniha\, R (University of Nottin
gham)
DTSTART;TZID=Europe/London:20140625T111500
DTEND;TZID=Europe/London:20140625T114500
UID:TALK53161AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/53161
DESCRIPTION:One may note that the symmetry-based methods were
not widely used for solving boundary-value problem
s (BVPs). To the best of our knowledge\, the first
rigorous definition of Lie's invariance for BVPs
was formulated by George Bluman in early 1970s and
applied to some classical BVPs.\n However\, Bluma
n's definition cannot be directly applied to BVPs
of more general form\, for example\, to those invo
lving boundary conditions on the moving surfaces\,
which are described by unknown functions. In our
recent papers\, a new definition of Lie's invarian
ce of BVP with a wide range of boundary conditions
(including those at infinity and moving surfaces)
was formulated. Moreover\, an algorithm of the gr
oup classification for the given class of BVPs was
worked out. The definition and algorithm were app
lied to some classes of nonlinear two-dimensional
and multidimensional BVPs of Stefan type with the
aim to show their efficiency. In particular\, the
group classification problem for these classes of
BVPs was solved\, reductions to BVPs of lower dime
nsionality were constructed and examples of exact
solutions with physical meaning were found.\n Very
recently\, the definition and algorithms were ext
ended on the case of conditional invariance for BV
Ps and applied to some nonlinear BVPs.\n This rese
arch was supported by a Marie Curie International
Incoming Fellowship within the 7th European Commun
ity Framework Programme.\n
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:Mustapha Amrani
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