物理学中普遍存在的线性连续方程的统一观点。第VII部分：边值和散射问题
A unifying perspective on linear continuum equations prevalent in physics. Part VII: Boundary value and scattering problems
摘要：
我们考虑空间或时空中有限范围的单连通体或区域，并在第一至第四部分写出与方程有关的守恒律。我们回顾以前的工作，椭圆方程，边界值问题被重新制定为一个问题的抽象理论的复合材料和相关的有效运营商等同于狄利克雷到诺依曼映射，管理机构的响应。介电极化率问题和声波和电磁散射的夹杂物制定的问题，在扩展的抽象理论的复合材料。散射响应可以由夹杂物上的适当积分来确定。
英文摘要：
We consider simply connected bodies or regions of finite extent in space or space-time and write conservation laws associated with the equations in Parts I-IV. We review earlier work where, for elliptic equations,the boundary value problem is reformulated as a problem in the abstract theory of composites and the associated effective operator is equated with the Dirichlet-to-Neumann map that governs the response of the body. The dielectric polarizability problem and acoustic and electromagnetic scattering by an inclusion are formulated as problems in the extended abstract theory of composites. The scattering response can be determined from appropriate integrals over the inclusion.
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