Academy of Mathematics and Systems Science, CAS Colloquia & Seminars
Speaker:
Dr. Haigang Li, Beijing Normal University
Inviter:
Pigong Han
Title:
Gradient estimates and asymptotics for elliptic equations from composite materials
Time & Venue:
2015.6.11 15:00-16:00 N613
Abstract:
Recently there is growing interest in partial differential equations with high contrast coefficients arising from the study of composite materials. In this talk, we consider the Lam\'e system with partially infinite coefficients which models a linear isotropic elastic body containing two adjoint inclusions with infinity elastic parameters. As the distance $\epsilon$ between the surfaces of discontinuity of the coefficients of the system tends to zero, we establish upper bounds on the blow up rate of the gradients of solutions. Especially, for strictly convex inclusions, we show the upper bound is $\epsilon^{-1/2}$, which is expected to be optimal, since the optimal bound for anti-plane elasticity is known to be $\epsilon^{-1/2}$ and some numerical results support this. For the simplified model----equation cases, we further obtain the asymptotic expression for the gradient of solutions. This talk is based on joint work with Professor Jiguang Bao and Yanyan Li.
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