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Partial differential equations of Classical Physics

Objective

I shall pursue two projects both of which belong to the fields of partial differential equations, geometric analysis and mathematical physics. The first project, ``the shock development problem", belongs also to the field of fluid dynamics and aims at a full understanding of how, in the real world of 3 spatial dimensions, hydrodynamic shocks evolve, my previous work having analyzed in detail how they form. The second project, ``the formation of electromagnetic shocks in nonlinear media" aims at establishing how electromagnetic shocks form by the focusing of incoming electromagnetic wave pulses in a nonlinear medium. The case of an isotropic nonlinear dielectric will be studied first, to be followed by the case of a general isotropic medium. The methods of geometric analysis introduced in my previous work shall be employed, in particular the ``short pulse method" introduced in my work on the formation of black holes by the focusing of incoming gravitational waves in general relativity. The application of these methods to the problem for a general isotropic medium will require the development of new geometric structures. My three Ph. D. students shall purse the following three projects, belonging also to the fields of partial differential equations, geometric analysis and mathematical physics. The first project is in nonlinear elasticity. It is the study of the equilibrium configurations, in free space, of a crystalline solid in which a continuous distribution of dislocations is present, and aims at analyzing the relationship between the dislocation distribution and the resulting internal stress field. The second is in general relativity and aims at a theoretical understanding of the phenomena discovered by M. Choptuik in his numerical study of the gravitational collapse of a self-gravitating scalar field in spherical symmetry. The third is the study of hydrodynamic shock interactions and focusing in spherical symmetry.

Field of science

  • /natural sciences/mathematics/pure mathematics/mathematical analysis/differential equations/partial differential equations
  • /natural sciences/physical sciences/astronomy/astrophysics/black hole
  • /natural sciences/physical sciences/classical mechanics/fluid mechanics/fluid dynamics
  • /natural sciences/mathematics/applied mathematics/mathematical physics
  • /natural sciences/physical sciences/astronomy/observational astronomy/gravitational waves

Call for proposal

ERC-2009-AdG
See other projects for this call

Funding Scheme

ERC-AG - ERC Advanced Grant

Host institution

EIDGENOESSISCHE TECHNISCHE HOCHSCHULE ZUERICH
Address
Raemistrasse 101
8092 Zuerich
Switzerland
Activity type
Higher or Secondary Education Establishments
EU contribution
€ 1 278 000
Principal investigator
Demetrios Christodoulou (Prof.)
Administrative Contact
Demetrios Christodoulou (Prof.)

Beneficiaries (1)

EIDGENOESSISCHE TECHNISCHE HOCHSCHULE ZUERICH
Switzerland
EU contribution
€ 1 278 000
Address
Raemistrasse 101
8092 Zuerich
Activity type
Higher or Secondary Education Establishments
Principal investigator
Demetrios Christodoulou (Prof.)
Administrative Contact
Demetrios Christodoulou (Prof.)