Analysis of p(x)-Laplace thermistor models describing the electrothermal behavior of organic semiconductor devices
Analysis of p(x)-Laplace thermistor models describing the electrothermal behavior of organic semiconductor devices
复制标题
描述有机半导体器件电热行为的 p(x)-拉普拉斯热敏电阻模型分析
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
M. Liero
中科院分区：
文献类型：
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作者：
A. Glitzky;M. Liero
本文研究了一个稳态热敏电阻模型，该模型描述了具有非欧姆电流-电压定律和自热效应的有机半导体器件的热行为。耦合系统由静电势的电流方程和以焦耳加热项为热源的热方程组成。在该设备中的自加热是由一个类似的温度依赖性的电导率Arrhenius建模。此外，非欧姆电行为由幂律建模，使得电导率非线性地依赖于电场。值得注意的是，我们允许不同的幂律函数的子结构，这导致了一个p（x）-拉普拉斯型问题，分段常数指数。我们证明了在二维情况下的解的存在性和有界性。关键的一点是建立静电势梯度的更高的可积性，以解决焦耳加热项。改进的正则性的证明是基于Caccioppoli型估计、Poincaré不等式和p（x）-Laplacian的Gehring型引理。最后利用Schauder不动点定理证明了解的存在性。
We study a stationary thermistor model describing the electrothermal behavior of organic semiconductor devices featuring non-Ohmic current-voltage laws and selfheating e↵ects. The coupled system consists of the current-flow equation for the electrostatic potential and the heat equation with Joule heating term as source. The self-heating in the device is modeled by an Arrhenius-like temperature dependency of the electrical conductivity. Moreover, the non-Ohmic electrical behavior is modeled by a power law such that the electrical conductivity depends nonlinearly on the electric field. Notably, we allow for functional substructures with di↵erent power laws, which gives rise to a p(x)-Laplace-type problem with piecewise constant exponent. We prove the existence and boundedness of solutions in the two-dimensional case. The crucial point is to establish the higher integrability of the gradient of the electrostatic potential to tackle the Joule heating term. The proof of the improved regularity is based on Caccioppoli-type estimates, Poincaré inequalities, and a Gehring-type Lemma for the p(x)-Laplacian. Finally, Schauder’s fixed-point theorem is used to show the existence of solutions.