振荡系数的Maxwell系统的透射特征值问题

he interior transmission eigenvalue problems (ITEPs) came originally from the scattering problems of incident waves for inhomogeneous media, which are the eigenvalue problems for elliptic equations with homogeneous coupling boundary conditions. Consider the ITEPs for Maxwell's equations of oscillatory refraction index with small period. Physically such kinds of problems govern the electromagnetic wave scattering in the media with inhomogeneous microstructure. We firstly explain the physical backgrounds for such kinds of nonstandard problems, showing that the eigenvalues are in fact the wave frequencies of incident waves for which the scattered waves vanish. Then by applying the homogenization process, we give the bounds on the transmission eigenvalues, prove that the eigenpairs for microstructure media converge to those of the homogenized system as the oscillating period goes to zero. The theoretical results provide a possible way to the efficient computations of the transmission eigenvalues of the Maxwell system with oscillating coefficient.