Cel Boundary value problems with moving boundaries are widely used in mathematical modeling a huge number of processes, which arise in physics, biology and industry. While these processes can be very different from a formal point of view, they have the common peculiarity: unknown moving boundaries. The most important subclass of such boundary value problems (BVPs) is the Stefan problems, in which the movement of unknown boundaries is governed by the well-known Stefan boundary conditions. BVPs with moving boundaries, particularly the multidimensional Stefan problems, are the main object of the proposed project.Developing new theoretical foundations and algorithms for reduction of such BVPs to those of lower dimensionality and construction of exact solutions of BVPs in question is the main aim of the project. Applied goal is to compare the analytical results derived with those obtained by means of the appropriate numerical techniques in the case of a wide range of the physically and biologically motivated problems. Moreover such comparison will demonstrate the real interdisciplinary aspect of the proposal. The novel idea of the project is to develop the algorithms mentioned above using such symmetry based methods as the classical Lie-Ovsiannikov method, the Bluman-Cole method of non-classical symmetry, conditional symmetry method and their recent extensions.The main results to be achieved: new definitions of (generalized) conditional invariance for BVPs with a wide range of boundary conditions will be derived; algorithms for how to construct all possible conditional symmetries for the given class of BVPs will be determined; new analytical results (conditional symmetries, reductions and exact solutions of BVPs) will be established by application of the algorithm to a wide range of nonlinear BVPs modeling the tumour growth processes and melting-evaporation processes. Dziedzina nauki natural sciencesmathematicsapplied mathematicsmathematical model Program(-y) FP7-PEOPLE - Specific programme "People" implementing the Seventh Framework Programme of the European Community for research, technological development and demonstration activities (2007 to 2013) Temat(-y) FP7-PEOPLE-2012-IIF - Marie Curie Action: "International Incoming Fellowships" Zaproszenie do składania wniosków FP7-PEOPLE-2012-IIF Zobacz inne projekty w ramach tego zaproszenia System finansowania MC-IIF - International Incoming Fellowships (IIF) Koordynator THE UNIVERSITY OF NOTTINGHAM Wkład UE € 270 580,80 Adres University Park NG7 2RD Nottingham Zjednoczone Królestwo Zobacz na mapie Region East Midlands (England) Derbyshire and Nottinghamshire Nottingham Rodzaj działalności Higher or Secondary Education Establishments Kontakt administracyjny Paul Cartledge (Mr.) Linki Kontakt z organizacją Opens in new window Strona internetowa Opens in new window Koszt całkowity Brak danych
