标题： 由以恒定速度运动的电介质产生的电磁波 显示英文标题

标题： Electromagnetic waves generated by a dielectric moving at a constant speed

摘要： 我们考虑一个规则且有界的电介质体以速度$|V|$移动，沿着常向量场$V$，相对于参考系。在此参考系中，狭义相对论表明通过构成方程推导出麦克斯韦系统，该构成方程将运动速度$|V|$与背景介质（例如真空）中的光速$c$联系起来。基于此模型，我们在自然情形下推导了相关正向散射问题的适定性，其中$\frac{|V|}{c}\leq C_{te}$且有一个适当的常数$C_{te} <1$，我们对其进行了估计。特别地，我们在该情形下证明了相关Lippmann-Schwinger系统的可逆性，并根据比率$\frac{|V|}{c}$表述了相应的Born级数。 作为应用，我们陈述并证明了在不知道运动速度的情况下，通过入射电磁波以速度$c$传播来照射介电体，可以唯一确定反问题的可识别性，即$|V|$或$V$。 这种可识别性结果在所考虑的条件下是有意义的。 显示英文摘要

摘要： We consider a regular and bounded dielectric body moving at a speed $|V|$, following a constant vector field $V$, with respect to a reference frame. In this frame, the special relativity implies that the Maxwell system is derived through the constitutive equations linking the moving speed $|V|$ and the speed of light $c$ in the background medium (as the vacuum for instance). Based on this model, we derive the well-poseness of the related forward scattering problem in the natural regime where $\frac{|V|}{c}\leq C_{te}$ with an appropriate constant $C_{te} <1$ that we estimate. In particular, we show the invertibility of the related Lippmann-Schwinger system in this regime and state the corresponding Born series in terms of the ratio $\frac{|V|}{c}$. As an application, we state and show the unique identifiability of the inverse problem of detecting the dielectric body, without knowing the moving speed $|V|$ or $V$, by illuminating it with incident electromagnetic waves propagating at the speed $c$. Such identifiability result makes sense in the regime under consideration.