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401-4767-66L  Partial Differential Equations (Hyperbolic PDEs)

SemesterAutumn Semester 2016
LecturersD. Christodoulou
Periodicitynon-recurring course
Language of instructionEnglish



Catalogue data

AbstractThe course begins with characteristics, the definition of hyperbolicity,
causal structure and the domain of dependence theorem. The course then focuses
on nonlinear systems of equations in two independent variables, in particular the
Euler equations of compressible fluids with plane symmetry and the Einstein equations
of general relativity with spherical symmetry.
ObjectiveThe objective is to introduce students in mathematics and physics to an area of
mathematical analysis involving differential geometry which is of fundamental importance
for the development of classical macroscopic continuum physics.
ContentThe course shall begin with the basic structure associated to hyperbolic
partial differential equations, characteristic hypersurfaces and bicharacteristics,
causal structure, and the domain of dependence theorem. The course shall then focus
on nonlinear systems of equations in two independent variables. The first topic shall be
the Euler equations of compressible fluids under plane symmetry where we shall
study the formation of shocks, and second topic shall be the Einstein equations
of general relativity under spherical symmetry where we shall study the formation of
black holes and spacetime singularities.
Prerequisites / NoticeBasic real analysis and differential geometry.

Performance assessment

Performance assessment information (valid until the course unit is held again)
Performance assessment as a semester course
ECTS credits7 credits
ExaminersD. Christodoulou
Typeend-of-semester examination
Language of examinationEnglish
RepetitionThe performance assessment is only offered at the end after the course unit. Repetition only possible after re-enrolling.
Additional information on mode of examinationOral, end of semester examination. Duration: 30 minutes.
Be aware that no exam repetition is offered.

Learning materials

No public learning materials available.
Only public learning materials are listed.

Courses

NumberTitleHoursLecturers
401-4767-66 VPartial Differential Equations (Hyperbolic PDEs)4 hrs
Mon13-15HG G 26.5 »
Wed10-12HG G 26.5 »
D. Christodoulou

Groups

No information on groups available.

Restrictions

There are no additional restrictions for the registration.

Offered in

ProgrammeSectionType
Doctoral Department of MathematicsGraduate SchoolWInformation
Mathematics MasterSelection: AnalysisWInformation
Physics MasterSelection: MathematicsWInformation