Weierstraß-Institut f ¨urAngewandte Analysis und Stochastik Leibniz-Institut im Forschungsverbund Berlin e. V. Preprint ISSN 2198-5855 An effective bulk-surface thermistor model for large-area organic light-emitting diodes Annegret Glitzky,Matthias Liero, Grigor Nika submitted: September 7, 2020 Weierstrass Institute Mohrenstr. 39 10117 Berlin Germany E-Mail:
[email protected] [email protected] [email protected] No. 2757 Berlin 2020 2010 Mathematics Subject Classification. 35Q79, 35J25, 80A20. Key words and phrases. Dimension reduced thermistor system, existence of weak solutions, entropy solutions, organic light emitting diode, self-heating. The authors gratefully acknowledge the funding by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy – The Berlin Mathematics Research Center MATH+ (EXC-2046/1, project ID: 390685689) in project AA2-1. Edited by Weierstraß-Institut fur¨ Angewandte Analysis und Stochastik (WIAS) Leibniz-Institut im Forschungsverbund Berlin e. V. Mohrenstraße 39 10117 Berlin Germany Fax: +49 30 20372-303 E-Mail:
[email protected] World Wide Web: http://www.wias-berlin.de/ An effective bulk-surface thermistor model for large-area organic light-emitting diodes Annegret Glitzky,Matthias Liero, Grigor Nika Abstract The existence of a weak solution for an effective system of partial differential equations describing the electrothermal behavior of large-area organic light-emitting diodes (OLEDs) is proved. The effective system consists of the heat equation in the three-dimensional bulk glass substrate and two semi-linear equations for the current flow through the electrodes coupled to algebraic equations for the continuity of the electrical fluxes through the organic layers.