Speaker: Prof. LI Haigang, School of Mathematical Sciences, Beijing Normal University
Tecent Meeting: https://meeting.tencent.com/s/0KNsIwrOer5X
Tecent Meeting ID: 408 379 459
A long-standing area of materials science research has been the study of electrostatic, magnetic, and elastic fields in composite with densely packed inclusions whose material properties differ from that of the background. For a general elliptic system, when the coefficients are piecewise H\”older continuous and uniformly bounded, an ε-independent bound of the gradient was obtained by Li and Nirenberg, where ε represents the distance between the interfacial surfaces. However, in high-contrast composites, when ε tends to zero, the stress always concentrates in the narrow regions. As a contrast to the uniform boundedness result of Li and Nirenberg, in order to investigate the role of ε played in such kind of concentration phenomenon, in this talk we will show the blow-up asymptotic expressions of the gradients of solutions to the Lame system with partially infinite coefficients in dimensions two and three. This completely solves the Babuska problem on blow-up analysis of stress concentration in high-contrast composite media. Recently, we extend our method to deal with the resonant behavior between two close-to-touching convex acoustic subwavelength resonators.