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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 threedimensional bulk glass substrate and two semilinear equations for the current flow through the electrodes coupled to algebraic equations for the continuity of the electrical fluxes through the organic layers. The electrical problem is formulated on the (curvilinear) surface of the glass substrate where the OLED is mounted. The source terms in the heat equation are due to Joule heating and are hence concentrated on the part of the boundary where the current-flow equation is posed. The existence of weak solutions to the effective system is proved via Schauder’s fixed-point theorem. Moreover, since the heat sources are a priori only in , the concept of entropy solutions is used.
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Annegret Glitzky, Matthias Liero, Grigor Nika, Analysis of a bulk-surface thermistor model for large-area organic LEDs. Port. Math. 78 (2021), no. 2, pp. 187–210DOI 10.4171/PM/2066