Communications in Mathematical Sciences

Volume 20 (2022)

Number 4

Quantitative spectral analysis of electromagnetic scattering. II: Evolution semigroups and non-perturbative solutions

Pages: 1025 – 1046



Yajun Zhou (Program in Applied and Computational Mathematics, Princeton University, Princeton, New Jersey, U.S.A.; and Academy of Advanced Interdisciplinary Studies (AAIS), Peking University, Beijing, China)


We carry out quantitative studies on the Green operator $\mathscr{\hat{G}}$ associated with the Born equation, an integral equation that models electromagnetic scattering, building the strong stability of the evolution semigroup $\lbrace \exp (i \tau G\mathscr{\hat{G}}) \vert \tau \geq 0 \rbrace$ on polynomial compactness and the Arendt–Batty–Lyubich–Vũ theorem. The strongly-stable evolution semigroup inspires our proposal of a nonperturbative method to solve the light scattering problem and improve the Born approximation.


electromagnetic scattering, Green operator, evolution semigroup, strong stability, non-perturbative solution

2010 Mathematics Subject Classification

35Q61, 45E99, 47B38, 47D06, 78A45

This research was supported in part by the Applied Mathematics Program within the Department of Energy (DOE) Office of Advanced Scientific Computing Research (ASCR) as part of the Collaboratory on Mathematics for Mesoscopic Modeling of Materials (CM4).

Received 7 January 2021

Received revised 12 October 2021

Accepted 25 October 2021

Published 11 April 2022