Department Mathematik



Mathematisches Kolloquium

Am Donnerstag, 02.11.2017, um 16:30 Uhr spricht

Dirk Deckert

im Hörsaal A027 über das Thema

N-body Problem of Classical Electrodynamics (Habilitationsvorstellung)

Zusammenfassung: I will report on a series of results on the solution theory of the coupled Maxwell and Lorentz equations describing the motion of N classical charges. I will start the discussion with a system of N rigid charges whose solutions can be obtained in terms of an initial value problem and explain the major obstacles in passing to the physically desirable point charge limit. In particular, I will demonstrate that already the Maxwell-Lorentz equations for point charges without self-interaction do not admit an initial value problem in the common sense as generic initial values lead to irregularities in the electromagnetic fields that travel along the light-cones of the initial charge positions and prevent global existence. Global smooth solutions can only be obtained by imposing an infinite system of constraints which effectively turn the Maxwell-Lorentz system into a system of delay differential equations. This system of delay equations is neutral, non-linear and involves state-dependent delays which renders its mathematical study very cumbersome. I will close with a discussion of recent results concerning existence and uniqueness of its solutions.
Alle Interessierten sind hiermit herzlich eingeladen. Eine halbe Stunde vor dem Vortrag gibt es Kaffee und Tee im Sozialraum (Raum 448) im 4. Stock.
Treffpunkt zum Abendessen um 18.00 Uhr wird noch bekannt gegeben.