Abstract

An inverse problem is considered for a system of semilinear elliptic equations that simulate radiative heat transfer with Fresnel matching conditions on the surfaces of discontinuity of the refractive index. The problem consists in finding the right-hand side of the heat equation, which is a linear combination of given functionals from their specified values on the solution. The solvability of the inverse problem is proved without restrictions on smallness. A sufficient condition for the uniqueness of the solution is presented.

中文翻译：

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菲涅耳匹配条件下复杂传热方程的反问题

摘要

对于半线性椭圆方程组，考虑了一个反问题，该方程组在折射率不连续的表面上模拟了具有菲涅耳匹配条件的辐射传热。问题在于找到热方程的右侧，该方程是从解上的给定函数根据其指定值进行的线性组合。证明了反问题的可解性，而对小度没有限制。提出了解决方案唯一性的充分条件。