WIAS Preprint No. 2757, (2020)

An effective bulk-surface thermistor model for large-area organic light-emitting diodes


  • Glitzky, Annegret
    ORCID: 0000-0003-1995-5491
  • Liero, Matthias
    ORCID: 0000-0002-0963-2915
  • Nika, Grigor
    ORCID: 0000-0002-4403-6908

2010 Mathematics Subject Classification

  • 35Q79 35J25 80A20


  • Dimension reduced thermistor system, existence of weak solutions, entropy solutions, organic light emitting diode, self-heating




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. 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 $L^1$, the concept of entropy solutions is used.

Appeared in

  • Port. Math., 78 (2021), pp. 187--210, DOI 10.4171/PM/2066 under the new title ''Analysis of a bulk-surface thermistor model for large-area organic LEDs" .

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