Sino-Russian Mathematics Center-JLU Colloquium (2026-009)—From Resonant Scatterers to PDE Control

Report Title：From Resonant Scatterers to PDE Control

Reporter： Mourad Sini

Affiliation: Austrian Academy of Sciences

Report Time:：May 11–18, 2026

Report Location:Zoom

Abstract:

This lecture series explores a control-theoretic use of small resonant scatterers in partial differential equations. The main idea is that suitably chosen micro-resonant inhomogeneities, such as bubbles or plasmonic nanoparticles, can be interpreted and designed as effective actuators for wave and heat equations. The first lecture introduces the general philosophy of the series: starting from physical resonance mechanisms, one derives effective point-actuator models of Foldy–Lax type and uses them to orient the analysis toward tracking and stabilization problems in control theory. The next two lectures develop this program in two representative settings, namely acoustic field generation by clusters of bubbles and heat generation by plasmonic nanoparticles. The final lecture synthesizes these case studies and discusses broader perspectives, including the use of reduced models for control design, direct control questions at the level of the original transmission problems, and possible extensions to other systems such as elasticity and other hybrid models. In this way, the series of lectures emphasizes that asymptotic reduction is the key step that connects resonance theory with PDE control.

Bio: 

M. Sini got his PhD degree from University of Provence, France, in October 2002. From September 2006, he joined the Radon Institute, of the Austrian Academy of Sciences, where he was tenured since 2011 as a senior fellow (equivalent to university professor) after securing the Habilitation degree from J. Kepler University in 2009. M. Sini was invited to deliver the IAAM Award Lecture (Sweden, August 2019) and an invited plenary speaker in the Applied Inverse Problems (AIP) conference (Grenoble, France, July 2019). He attracted around 2 Mi euro as third-party funding. M. Sini is interested in the analysis of partial differential equations applied to inverse problems, mathematical imaging, mathematical therapy and material theory. By now, he published nearly 100 papers, most of them in top journals, several book chapters and co-edited a book.  He is member of the editorial board of several journals including Mathematical Methods in Applied Sciences (Wiley) and Communication on Analysis and Computation (AIMS).