  The forward problem here is the Cauchy problem for a 1D hyperbolic PDE with a
variable coefficient in the principal part of the operator. That coefficient is
the spatially distributed dielectric constant. The inverse problem consists of
the recovery of that dielectric constant from backscattering boundary
measurements. The data depend on one variable, which is time. To address this
problem, a new version of the convexification method is analytically developed.
The theory guarantees the global convergence of this method. Numerical testing
is conducted for both computationally simulated and experimental data.
Experimental data, which are collected in the field, mimic the problem of the
recovery of the spatially distributed dielectric constants of antipersonnel
land mines and improvised explosive devices.
