HYDRON

Near Hydrodynamic Type Systems in 2 +1 Dimensions

Coordinatore	GEORG-AUGUST-UNIVERSITAET GOETTINGEN STIFTUNG OEFFENTLICHEN RECHTS    more  Organization address address: WILHELMSPLATZ 1 city: GOTTINGEN postcode: 37073 contact info Titolo: Ms. Nome: Nadja Cognome: Daghbouche Email: send email Telefono: +49 551 399795 Fax: +49 551 39189795
Nazionalità Coordinatore	Germany [DE]
Totale costo	161˙968 €
EC contributo	161˙968 €
Programma	FP7-PEOPLE Specific programme "People" implementing the Seventh Framework Programme of the European Community for research, technological development and demonstration activities (2007 to 2013)
Code Call	FP7-PEOPLE-2012-IEF
Funding Scheme	MC-IEF
Anno di inizio	2013
Periodo (anno-mese-giorno)	2013-06-01   -   2015-05-31

 Partecipanti

#	participant	country	role	EC contrib. [€]
1	GEORG-AUGUST-UNIVERSITAET GOETTINGEN STIFTUNG OEFFENTLICHEN RECHTS  Organization address address: WILHELMSPLATZ 1 city: GOTTINGEN postcode: 37073 contact info Titolo: Ms. Nome: Nadja Cognome: Daghbouche Email: send email Telefono: +49 551 399795 Fax: +49 551 39189795	DE (GOTTINGEN)	coordinator	161˙968.80

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 Obiettivo del progetto (Objective)

'Systems of hydrodynamic type are first-order quasi-linear PDEs (partial differential equations). Their solutions are generically singular. As certain limits of more general nonlinear PDEs, modelling e.g. the evolution of physical systems, they describe critical phenomena, like shock waves. An embedding in (or deformation to) a more general nonlinear PDE typically 'regularises' such a critical phenomenon and introduces specific features. The question how such a catastrophe becomes noticeable near a corresponding critical event is of uttermost importance, in particular for its prediction in nature. Moreover, explorations in 11 space-time dimensions led to a conjecture (Boris Dubrovin, 2006) of a universal behavior of solutions near such critical events, governed by an exceptional class of differential equations, the Painleve equations. In this project, hydrodynamic-type systems are addressed as limiting cases of integrable PDEs, for which a large class of exact solutions can be constructed and powerful analytical methods are available. It concentrates on equations in 21 space-time dimensions, which in this respect is fairly unexplored terrain. Three complementary methods are employed for a corresponding exploration: hydrodynamic reductions, bidifferential calculus, and numerical analysis in the critical regime.'