Inverse Problems for Hyperbolic Equations

Abstract

In the first part of this chapter we study two inverse source problems related to the second order hyperbolic equations $u_{tt}-u_{xx}=\rho (x, t)g(t)$ and $u_{tt}-u_{xx}=\rho (x, t)\varphi (x)$ for the quarter plane $\mathbb {R}^2_+=\{(x, t)|\, x>0, t>0\}$, with Dirichlet type measured output data $f(t):=u(x, t)\vert _{x=0}$.