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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Hyperbolicity and boundary conditions. - Oscar Reu
 la (Universidad Nacional de Córdoba)
DTSTART;TZID=Europe/London:20191001T133000
DTEND;TZID=Europe/London:20191001T143000
UID:TALK130567AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/130567
DESCRIPTION:Abstract: (In collaboration with Fernando Abalos.)
  Very often in physics\, the evolution systems we 
 have to deal with are not purely hyperbolic\, but 
 contain also constraints and gauge freedoms. After
  fixing these gauge freedoms we obtain a new syste
 m with constraints which we want to solve subject 
 to initial and boundary values. In particular\, th
 ese values have to imply the correct propagation o
 f constraints. In general\, after fixing some redu
 ction to a purely evolutionary system\,  this is a
 sserting by computing by hand what is called the c
 onstraint subsidiary system\, namely a system whic
 h is satisfied by the constraints quantities when 
 the fields satisfy the reduced evolution system.<b
 r> If the subsidiary system is also hyperbolic the
 n for the initial data case the situation is clear
 : we need to impose the constraints on the initial
  data and then they will correctly propagate along
  evolution. For the boundary data\, we need to imp
 ose the constraint for all incoming constraint mod
 es. These must be done by fixing some of the other
 wise free boundary data\, that is the incoming mod
 es. Thus\, there must be a relation between some o
 f the incoming modes of the evolution system and a
 ll the incoming modes of the constraint subsidiary
  system. Under certain conditions on the constrain
 ts\, this relation is known and understood\, but t
 hose conditions are very restrictive. In this talk
 \, we shall review the known results and discuss w
 hat is known so far for the general case and what 
 are the open questions that still remain. <br>
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:INI IT
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