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SUMMARY:Symmetries of Boundary Value Problems: Definitions\, Algorithms an
 d Applications to Physically Motivated Problems - Cherniha\, R (University
  of Nottingham)
DTSTART:20140625T101500Z
DTEND:20140625T104500Z
UID:TALK53161@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:One may note that the symmetry-based methods were not widely u
 sed for solving boundary-value problems (BVPs). To the best of our knowled
 ge\, the first rigorous definition of Lie's invariance for BVPs was formul
 ated by George Bluman in early 1970s and applied to some classical BVPs.\n
  However\, Bluman's definition cannot be directly applied to BVPs of more 
 general form\, for example\, to those involving boundary conditions on the
  moving surfaces\, which are described by unknown functions. In our recent
  papers\, a new definition of Lie's invariance of BVP with a wide range of
  boundary conditions (including those at infinity and moving surfaces) was
  formulated. Moreover\, an algorithm of the group classification for the g
 iven class of BVPs was worked out. The definition and algorithm were appli
 ed 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\, reduct
 ions to BVPs of lower dimensionality were constructed and examples of exac
 t solutions with physical meaning were found.\n Very recently\, the defini
 tion and algorithms were extended on the case of conditional invariance fo
 r BVPs and applied to some nonlinear BVPs.\n This research was supported b
 y a Marie Curie International Incoming Fellowship within the 7th European 
 Community Framework Programme.\n
LOCATION:Seminar Room 1\, Newton Institute
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