Séminaire de groupe
|Lie symmetries and reductions of boundary value problems of the Stefan type|
|Dpt. Maths, Ukr Acad. Sciences, Kyiv, Ukraine|
|vendredi 28 octobre 2011 , 14h15|
|Salle de séminaire du groupe de Physique Statistique|
A new definition of Lie-invariance for nonlinear multidimensional boundary value problems (BVPs) is proposed by the generalisation of existing those on much wider class of BVPs. The class of (1+3)-dimensional nonlinear BVPs of the Stefan type modeling the process of melting and evaporation of metals is studied in details. Using the definition proposed, the group classification problem for this class of BVPs is solved and some reductions (with physical meaning) to BVPs of lower dimensionality are constructed. An example how to construct exact solution of the (1+3)-dimensional nonlinear BVP problem with correctly-specified coeffcients is presented.