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SUMMARY:Hyperbolicity and boundary conditions. - Oscar Reula (Universidad 
 Nacional de Córdoba)
DTSTART:20191001T123000Z
DTEND:20191001T133000Z
UID:TALK130570@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:Abstract: (In collaboration with Fernando Abalos.) Very often 
 in physics\, the evolution systems we have to deal with are not purely hyp
 erbolic\, but contain also constraints and gauge freedoms. After fixing th
 ese gauge freedoms we obtain a new system with constraints which we want t
 o solve subject to initial and boundary values. In particular\, these valu
 es have to imply the correct propagation of constraints. In general\, afte
 r fixing some reduction to a purely evolutionary system\,  this is asserti
 ng by computing by hand what is called the constraint subsidiary system\, 
 namely a system which is satisfied by the constraints quantities when the 
 fields satisfy the reduced evolution system.<br> If the subsidiary system 
 is also hyperbolic then for the initial data case the situation is clear: 
 we need to impose the constraints on the initial data and then they will c
 orrectly propagate along evolution. For the boundary data\, we need to imp
 ose the constraint for all incoming constraint modes. These must be done b
 y fixing some of the otherwise free boundary data\, that is the incoming m
 odes. Thus\, there must be a relation between some of the incoming modes o
 f the evolution system and all the incoming modes of the constraint subsid
 iary system. Under certain conditions on the constraints\, this relation i
 s known and understood\, but those conditions are very restrictive. In thi
 s talk\, we shall review the known results and discuss what is known so fa
 r for the general case and what are the open questions that still remain. 
 <br>
LOCATION:Seminar Room 1\, Newton Institute
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