Analysis of the controllability from the exterior of strong damping nonlocal wave equations
Abstract
We make a complete analysis of the controllability properties from the exterior of the (possible) strong damping wave equation associated with the fractional Laplace operator subject to the non-homogeneous Dirichlet type exterior condition. In the first part, we show that if 0 sN(N≥ 1) is a bounded Lipschitz domain and the parameterδ> 0, then there is no control functiongsuch that the following system\begin{align} u_{1,n}+ u_{0,n}\widetilde{\lambda}_{n}^++ \delta u_{0,n}\lambda_{n}=\int_0^{T}\int_{\Omc}(g(x,t)+\delta g_t(x,t))e^{-\widetilde{\lambda}_{n}^+ t}\mathcal{N}_{s}\varphi_{n}(x)\d x\d t,\label{39}\\ u_{1,n}+ u_{0,n}\widetilde{\lambda}_{n}^- +\delta u_{0,n}\lambda_{n}=\int_0^{T}\int_{\Omc}(g(x,t)+\delta g_t(x,t))e^{-\widetilde{\lambda}_{n}^- t}\mathcal{N}_{s}\varphi_{n}(x)\d x\d t,\label{40} \end{align}
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Jan 01, 2020
- Source ID
- 10.1051/cocv/2019028
Entities
People
- Mahamadi Warma
- Sebastián Zamorano
Organizations
- Air Force Office of Scientific Research