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SUMMARY:Essential spectra and spectral pollution for Maxwell and Drude-Lor
 entz systems - Marco Marletta (Cardiff University)
DTSTART:20231026T140000Z
DTEND:20231026T150000Z
UID:TALK207637@talks.cam.ac.uk
CONTACT:Matthew Colbrook
DESCRIPTION:In order to discuss uniqueness of solutions to inverse problem
 s for inhomogeneous Maxwell systems with conductivity\, it is useful to ha
 ve good a-priori estimates of where the spectra of such systems lies\; in 
 order to solve the spectral problems numerically\, one needs to understand
  how much of a problem spectral pollution may be. A priori one expects the
 se problems to be greatly complicated by features such as the well known l
 ack of coercivity\, and consequent low regularity of solutions\, for Maxwe
 ll and Drude-Lorentz systems. The fact that Drude-Lorentz systems are also
  nonlinear in the spectral parameter adds a further layer of interest. The
  investigation of these problems reveals many more interesting questions a
 nd \nphenomena. Plasmon-type quasi-modes concentrated around discontinuity
  interfaces (black hole quasi-modes) may characterise one of the component
 s of the essential spectrum. Spectral pollution turns out to be confined t
 o a much smaller set than anyone had dared expect. Resolvent estimates are
  possible using an abstract Morawetz-type trick.\n\nThis talk discusses wo
 rk with co-authors including Giovanni Alberti (Genova)\,\nSabine Boegli (D
 urham)\, Malcolm Brown (Cardiff\; deceased) Francesco Ferraresso (Sassari)
 \,\nChristiane Tretter (Bern) and Ian Wood (Kent).\n
LOCATION:Centre for Mathematical Sciences\, MR14
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