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Analysis of p(x)-Laplace thermistor models describing the electrothermal behavior of organic semiconductor devices

Please always quote using this URN:urn:nbn:de:0296-matheon-13699
  • We study a stationary thermistor model describing the electrothermal behavior of organic semiconductor devices featuring non-Ohmic current-voltage laws and self-heating effects. 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 different 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, Poincar\'e 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.

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Metadaten
Author:Annegret Glitzky, Matthias Liero
URN:urn:nbn:de:0296-matheon-13699
Referee:Frank Schmidt
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2016/02/04
Release Date:2016/02/04
Tag:Thermistor model, p(x)-Laplacian, nonlinear coupled system, existence and boundedness, regularity theory, Caccioppoli estimates, organic light emitting diode, self-heating, Arrhenius like conductivity law
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 / 35Bxx Qualitative properties of solutions / 35B65 Smoothness and regularity of solutions
35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Jxx Elliptic equations and systems [See also 58J10, 58J20] / 35J57 Boundary value problems for second-order elliptic systems
35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Jxx Elliptic equations and systems [See also 58J10, 58J20] / 35J92 Quasilinear elliptic equations with p-Laplacian
80-XX CLASSICAL THERMODYNAMICS, HEAT TRANSFER (For thermodynamics of solids, see 74A15) / 80Axx Thermodynamics and heat transfer / 80A20 Heat and mass transfer, heat flow
Preprint Number:1100
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