摘要
In this paper,we establish a novel unique continuation property for two-dimensional anisotropic elasticity systems with partial information.More precisely,given a homogeneous elasticity system in a connected open bounded domain,we investigate the unique continuation by assuming only the vanishing of one component of the solution in a subdomain.Using the corresponding Riemann function,we prove that the solution vanishes in the whole domain provided that the other component vanishes at one point up to its second derivatives.Further,we construct several examples showing the possibility of further reducing the additional information of the other component.This result possesses remarkable significance in both theoretical and practical aspects because the required data are almost halved for the unique determination of the whole solution.
基金
supported by the A3 Foresight Program“Modeling and Computation of Applied Inverse Problems”
Japan Society for the Promotion of Science(JSPS)
National Natural Science Foundation of China(NSFC)
supported by NSFC(No.11971121)
partially supported by JSPS KAKENHI Grant Number JP15H05740
supported by NSFC(No.11771270)
partly supported by NSFC(No.91730303)
RUDN University Program5-100。
