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.
All Science Journal Classification (ASJC) codes
- Computational Mathematics
- Applied Mathematics