Unique Continuation Property with Partial Information for Two-Dimensional Anisotropic Elasticity Systems

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 vanishin...

Full description

Saved in:
Bibliographic Details
Published inActa Mathematicae Applicatae Sinica Vol. 36; no. 1; pp. 3 - 17
Main Authors Cheng, Jin, Liu, Yi-kan, Wang, Yan-bo, Yamamoto, Masahiro
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 2020
Springer Nature B.V
EditionEnglish series
Subjects
Anisotropy
Applications of Mathematics
Elasticity
Math Applications in Computer Science
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Theoretical
anisotropic elasticity system
Riemann function
74B05
35B60
unique continuation
Online AccessGet full text

Cover

More Information
Summary: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.
ISSN:0168-9673
1618-3932
DOI:10.1007/s10255-020-0910-y