Unique continuation property for a coupled second-fourth order dynamical system and its application

Ching Lung Lin, Gen Nakamura

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper we consider a coupled second-fourth order dynamical system. In this coupled system, there are two types of hyperbolic operators in the principal part. We first use the localized Fourier-Gauss transformation to change the coupled second-fourth order dynamical system to a coupled second-fourth order system with two types of elliptic operators in the principal part. After that we derive Carleman-type estimates for the two types of elliptic operators with same weights and apply it to prove the unique continuation property (UCP) of the solution. Using the UCP, we can extend the Dirichlet-to-Neumann map given for large enough time interval to the infinite time interval. We also give some application to the data analysis of the nondestructive testing of steel-concrete connected beams.

Original languageEnglish
Pages (from-to)2318-2336
Number of pages19
JournalSIAM Journal on Mathematical Analysis
Volume42
Issue number5
DOIs
Publication statusPublished - 2010 Oct 26

All Science Journal Classification (ASJC) codes

  • Analysis
  • Computational Mathematics
  • Applied Mathematics

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