S. Rikte, EXISTENCE, UNIQUENESS, AND CAUSALITY THEOREMS FOR WAVE-PROPAGATION INSTRATIFIED, TEMPORALLY DISPERSIVE, COMPLEX MEDIA, SIAM journal on applied mathematics, 57(5), 1997, pp. 1373-1389
A mixed initial-boundary value problem for a nonlocal, hyperbolic equa
tion is analyzed with respect to unique solubility and causality. The
regularity of the step response and impulse response (the Green functi
ons) is investigated, and a wave front theorem is proved. The problem
arises, e.g., at time-varying, electromagnetic, plane wave excitation
of stratified, temporally dispersive, bi-isotropic or anisotropic slab
s. Concluding, the problem is uniquely solvable, strict causality hold
s, and a well-defined wave front speed exists. This speed is independe
nt of dispersion and excitation, and depends on the nondispersive prop
erties of the medium only.