In this talk, we establish the well-posedness of the micro-cell problems associated with a multiscale model for electromagnetic media derived by Blanco et al. in the paper A novel multiscale model for micro-structured electromagnetic media, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 480:20240495, 2024.
We also demonstrate a Poincar ́e type inequality under irregular setting. The results obtained can be fundamental for justifying the multiscale model mathematically in the future. This talk is based on the joint work with Prof. P. J. Blanco and Prof. A. A. Novotny, Submitted in Bull. London Math. Soc.
Dr. Ravi Prakash is an Associate Professor in the Department of Mathematics, University of Concepción, Concepción, Chile. He earned his Ph.D. from the Indian Institute of Science (IISc), Bengaluru, and subsequently carried out postdoctoral research in India, France, Chile, and Brazil. His research focuses on partial differential equations, particularly inverse problems, optimal control, and homogenization, with applications in imaging, materials science, and biomedical modeling.
He is currently visiting IIT Madras.
