热电方程的极限模型
A limit model for thermoelectric equations
摘要：
我们分析了热电器件中任意高导热率对应的渐近行为。本文研究了稳态多维热敏电阻问题，考虑了焦耳效应和空间与温度相关的输运系数，在某些实际边界条件下，考虑了Seebeck-Peltier-Thomson交叉效应。我们的第一个目的是，存在一个弱解的数据，特别是在非光滑域的最小假设下成立。在不同的电导率假设条件下，研究了两个解的存在性。他们的证明是基于一个不动点参数，紧性方法，存在性和正则性理论的椭圆标量方程。第二个目的是证明极限模型的存在性，说明渐近情况。
英文摘要：
We analyze the asymptotic behavior corresponding to the arbitrary high conductivity of the heat in the thermoelectric devices. This work deals with a steady-state multidimensional thermistor problem, considering the Joule effect and both spatial and temperature dependent transport coefficients under some real boundary conditions in accordance with the Seebeck-Peltier-Thomson cross-effects. Our first purpose is that the existence of a weak solution holds true under minimal assumptions on the data, as in particular nonsmooth domains. Two existence results are studied under different assumptions on the electrical conductivity. Their proofs are based on a fixed point argument, compactness methods, and existence and regularity theory for elliptic scalar equations. The second purpose is to show the existence of a limit model illustrating the asymptotic situation.
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