Uniqueness for an inverse problem for the wave equation in the half space
Consider the initial and boundary value problem \[ u_{tt}-\Delta_xu+ b(x)u_t+a(x)u=0,\quad\text{in }\mathbb{R}^n_+\times(0,T), \] \[ u=u_t=0\quad\text{on }\mathbb{R}^n_+\times\{0\},\;\partial_zu(y,0,t)=f(y,t)\quad\text{on }\mathbb{R}^{n-1}\times(0,T). \] Here, \(a\) is bounded, \(b\) is \(C^2\) smooth and both \(a\) and \(b\) are assumed to be constant for \(|x|>r\). The author proves that for \(T>(\pi+1)r\), the Neumann-to-Dirichlet map uniquely determines the coefficients \(a\) and \(b\).
scientific article; zbMATH DE number 927042