Back to Search
Start Over
Unique Continuation Property with Partial Information for Two-Dimensional Anisotropic Elasticity Systems
- Source :
- Acta Mathematicae Applicatae Sinica, English Series. 36:3-17
- Publication Year :
- 2019
- Publisher :
- Springer Science and Business Media LLC, 2019.
-
Abstract
- 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 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 is almost halved for the unique determination of the whole solution.<br />14 pages, 1 figure
- Subjects :
- Applied Mathematics
010102 general mathematics
Mathematical analysis
Riemann function
Elasticity (physics)
anisotropic elasticity system
unique continuation
74B05, 35B60
01 natural sciences
010101 applied mathematics
Continuation
Riemann hypothesis
symbols.namesake
Mathematics - Analysis of PDEs
Homogeneous
Bounded function
FOS: Mathematics
symbols
0101 mathematics
Anisotropic elasticity
Analysis of PDEs (math.AP)
Second derivative
Mathematics
Subjects
Details
- ISSN :
- 16183932 and 01689673
- Volume :
- 36
- Database :
- OpenAIRE
- Journal :
- Acta Mathematicae Applicatae Sinica, English Series
- Accession number :
- edsair.doi.dedup.....f5c4076ca20ee122aa374ea439e68812