On an inverse initial-boundary value problem for a one-dimensional hyperbolic system of differential equations (Q1363010)

The authors discuss the following inverse boundary value problem in the frequency domain: \[ \Biggl({\partial\over\partial t}+{\partial\over\partial x}\Biggr) u_1(x, t)= -b(x)u_2(x, t),\quad \Biggl({\partial\over\partial t}+ {\partial\over\partial x}\Biggr) u_1(x, t)= b(x)u_1(x, t),\quad t,x>0 \] \[ u_1(0, t)= -u_2(0, t)=\widetilde f(t),\quad u_1(x, 0)= -\delta(x),\quad u_2(x, 0)= \delta(x). \] The problem is to determine \(b(x)\) from the impulse response \(\widetilde f(t)\). The estimate of the solution and the quantitative analysis about its stability are obtained, and some stability criteria are established.