Thermistor systems of p(x)-Laplace-type with discontinuous exponents via entropy solutions
Please always quote using this URN:urn:nbn:de:0296-matheon-13914
- We show the existence of solutions to a system of elliptic PDEs, that was recently introduced to describe the electrothermal behavior of organic semiconductor devices. Here, two difficulties appear: (i) the elliptic term in the current-flow equation is of $p(x)$-Laplacian-type with discontinuous exponent $p$, which limits the use of standard methods, and (ii) in the heat equation, we have to deal with an a priori $L^1$ term on the right hand side describing the Joule heating in the device. We prove the existence of a weak solution under very weak assumptions on the data. Our existence proof is based on Schauder’s fixed point theorem and the concept of entropy solutions for the heat equation. Here, the crucial point is the continuous dependence of the entropy solutions on the data of the problem.
Author: | Miroslav Bulíček, Annegret Glitzky, Matthias Liero |
---|---|
URN: | urn:nbn:de:0296-matheon-13914 |
Referee: | Frank Schmidt |
Document Type: | Preprint, Research Center Matheon |
Language: | English |
Date of first Publication: | 2016/11/23 |
Release Date: | 2016/11/23 |
Tag: | Sobolev spaces with variable exponent, existence of weak solution, entropy solution, thermistor system, p(x)-Laplacian, heat transfer |
Institute: | Weierstraß-Institut für Angewandte Analysis und Stochastik (WIAS) |
Project: | D Optics and Electronics (Electronic and photonic devices) / D-SE2 Electrothermal modeling of large-area OLEDs |
MSC-Classification: | 35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Jxx Elliptic equations and systems [See also 58J10, 58J20] / 35J92 Quasilinear elliptic equations with p-Laplacian |
Preprint Number: | 1111 |