Akce ČVUT

MAFIA Seminar: Borbala Gerhat (University of Bern / Queen's University Belfast)-Schur complement dom

12.12.2019   13:15

Srdečně vás zveme na poslední letošní MAFIA Seminar na KM FJFI. Seminář se koná od 13.15 hodin v místnosti T112.

Abstract:
In mathematical physics, matrix (differential) operators arise naturally in applications as coupled systems of partial differential equations. Up to now, the spectral analysis of such problems has typically been tackled by means of perturbation theory. We propose to view operator matrices in a more general setting, which allows our results to fully abstain from any perturbative argument.
Rather than requiring the matrix to act in a Hilbert space H, we extend its action to a suitable distributional triple D H D0 and restrict it to its maximal domain in H. The crucial point in our approach is the choice of the spaces D and D0 which are essentially determined by the Schur complement of the matrix. We show spectral equivalence between the resulting operator matrix in H and its Schur complement, eventually implying closedness and non-empty resolvent set of the matrix. Finally, we apply our abstract results to the damped wave equation with possibly unbounded and singular damping, as well as to more general second order matrix differential operators with singular coefficients. By means of our methods, the previously used regularity assumptions can be lowered substantially in both cases.

Místo konání

Budova FJFI ČVUT, Trojanova 13, Praha 2

Pořadatel

Fakulta jaderná a fyzikálně inženýrská ČVUT v Praze

Kontaktní osoba

Ing. Matěj Tušek, Ph.D., matej.tusek@fjfi.cvut.cz