Causality and restrictions on the initial-boundary conditions for signal propagation in attenuating medium

To investigate the propagation of nonsinusoidal signal in a bounded attenuating medium, it is generally required to solve the 2nd order hyperbolic partial differential equation (PDE) with specified initial-boundary conditions (IBCs). Because of the lack of well-posed conditions of such PDE system, some problems aroused in such system, referred to as Harmuth´s (1986) problem, relating to the validity of Maxwell´s equations for signal propagation in attenuating media. Previous investigations on the equivalence between the magnetic and electric sources in attenuating medium shows that similar problem arises. Mathematically, the problem is essentially restricted to the case whether we can give a complete solutions, including the associated magnetic (electric) propagation for electric (magnetic) excitation, for some specified signal such as the step function signal or the exponential ramp signal since for many other excitations, the equations with corresponding IBCs can be solved successfully. The lack of well-posed conditions baffles a comprehensive solving of the problem and has led to different solving techniques to give a unique and causal solution in practice. By investigating the restrictions on the IBCs due to the causality requirement, supplement requirements on the IBCs of the 2nd order hyperbolic PDE, though does not mean the well-posed IBCs, can be offered to help the evaluation of Harmuth´s modification to Maxwell´s equations.