论文标题
各向同性非自主热流的逆边界值问题
An inverse boundary value problem for isotropic nonautonomous heat flows
论文作者
论文摘要
我们研究了一个逆边界价值问题，以确定各向同性非自治热流中的主要秩序系数，如下所示；在介质的情况下，在没有热源和水槽的情况下，是否可以从温度和热通量测量的边界上的库奇数据数据中唯一确定培养基的时间依赖的热导率和体积热容量？在对介质的热扩散性的假设下，我们在所有维度上都证明了唯一性，该假设定义为热导率和容积热容量的比率。作为我们各向同性培养基的结果的推论，我们在二维各向异性培养基中还获得了独特的结果，直至自然量表。我们对热扩散率的假设与某些指数溶液对热方程的构建有关。
We study an inverse boundary value problem on the determination of principal order coefficients in isotropic nonautonomous heat flows stated as follows; given a medium, and in the absence of heat sources and sinks, can the time-dependent thermal conductivity and volumetric heat capacity of the medium be uniquely determined from the Cauchy data of temperature and heat flux measurements on its boundary? We prove uniqueness in all dimensions under an assumption on the thermal diffusivity of the medium, which is defined as the ratio of the thermal conductivity and volumetric heat capacity. As a corollary of our result for isotropic media, we also obtain a uniqueness result, up to a natural gauge, in two-dimensional anisotropic media. Our assumption on the thermal diffusivity is related to construction of certain families of exponential solutions to the heat equation.
