Events for 04/13/2022 from all calendars

Mathematical Physics and Harmonic Analysis Seminar

Time: 09:00AM - 10:00AM

Location: Zoom

Speaker: Yulia Ershova

Title: Zero-range models with internal structure in the analysis of strongly inhomogenous media

Abstract: In this talk, I will consider a prototype large-coupling transmission problem, posed on a bounded domain, containing a "low-index" inclusion located at a positive distance to the boundary. Mathematically, this is modelled by a "weighted" Laplacian, where the weight on the containing domain is 1 and the weight on the inclusion is assumed to be large ("high contrast"). This is supplemented by the Neumann boundary condition on the outer boundary and "natural" continuity conditions on the interface (i.e., the inclusion boundary).

A formal asymptotic argument suggests that eigenvalues of this operator should converge to those of the so-called "electrostatic problem" (although the existing results do not quite yield spectral convergence). Our operator-theoretic approach based on our analysis of critical-contrast periodic composites, allows one to improve these results in two respects: (a) our estimates are of the operator-norm resolvent type, implying, in particular, the uniform convergence of the associated spectra in any compact set; (b) our estimates are uniform with respect to the contrast parameter and are order-sharp, i.e. the rate of convergence in terms of the contrast cannot be improved further.

Based on joint work with Cherednichenko, Kiselev and Silva.

URL: Event link

Committee P Meeting

Time: 4:00PM - 5:00PM

Location: BLOC 117

Committee P & IP Meeting

Time: 4:00PM - 5:00PM

Location: BLOC 117