一类具有幂型边界效应的热电问题的弱解
Weak solutions for a thermoelectric problem with power-type boundary effects
摘要：
本文讨论了包括Peltier效应和Seebeck效应在内的热电问题。耦合的椭圆和双拟线性抛物型方程的电流和热流的陈述，分别完成与功率型边界条件，描述的热辐射效应。为了验证这个耦合问题的弱解的存在性（定理1），本文给出了具有非光滑数据的抽象多拟线性椭圆抛物方程组的解析研究（定理2和3）.它们基本上是基于Rothe方法的近似解。它包括引入时间离散化问题，建立它们的存在性，然后随着时间步长趋于零而传递到极限。时间离散解的存在性的证明依赖于不动点和紧性参数。在这项研究中，我们建立了定量估计，以澄清小的条件。
英文摘要：
This paper deals with thermoelectric problems including the Peltier and Seebeck effects. The coupled elliptic and doubly quasilinear parabolic equations for the electric and heat currents are stated, respectively, accomplished with power-type boundary conditions that describe the thermal radiative effects. To verify the existence of weak solutions to this coupled problem (Theorem 1), analytical investigations for abstract multi-quasilinear elliptic-parabolic systems with nonsmooth data are presented (Theorem 2 and 3). They are essentially approximated solutions based on the Rothe method. It consists on introducing time discretized problems, establishing their existence, and then passing to the limit as the time step goes to zero. The proof of the existence of time discretized solutions relies on fixed point and compactness arguments. In this study, we establish quantitative estimates to clarify the smallness conditions.
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