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X-ORIGINAL-URL:https://matematica.unipv.it/
X-WR-CALNAME:Dipartimento di Matematica UNIPV
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BEGIN:VEVENT
CLASS:PUBLIC
UID:MEC-236522d75c8164f90a85448456e1d1aa@matematica.unipv.it
DTSTART:20161019T130000Z
DTEND:20161019T140000Z
DTSTAMP:20201209T083200Z
CREATED:20201209
LAST-MODIFIED:20210114
PRIORITY:5
TRANSP:OPAQUE
SUMMARY:Lagrangian representation for conservation laws
DESCRIPTION:Lagrangian representation for conservation laws\nProf. Stefano Bianchini, SISSA, Trieste\nThe use of characteristics to represent smooth solutions in quasilinear first order systems is textbook classic, and it is also well known that after the so called gradient catastrophe, this representation fails because the solution becomes discontinuous and there is no canonical way to continue the representation. For linear transport equations, instead, even if the solution is very weak (say a measure) and the vector field is only locally integrable, a representation in terms of superposition of characteristics is the base of important progresses regarding uniqueness and existence of a more regular flow.\nIn this talk I will show how the method of characteristic can be extended to scalar equations and hyperbolic systems of conservation laws, yielding a new representation of the solution, the Lagrangian representation. I will address in particular the following points:\n\nquestions where the Lagrangian representation arises naturally;\nthe Lagrangian representation as a continuous wave tracing;\nfine description of $L^\infty$-solutions for scalar equations and $BV$-solutions for systems.\n\n
URL:https://matematica.unipv.it/events/lagrangian-representation-for-conservation-laws/
ORGANIZER;CN=Prof. Stefano Bianchini (SISSA, Trieste):MAILTO:
CATEGORIES:Colloquium Magenes
LOCATION:Sala conferenze IMATI-CNR
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