Glitzky, Annegret; Liero, Matthias; Nika, Grigor Dimension reduction of thermistor models for large-area organic light-emitting diodes. (English) Zbl 1481.35239 Discrete Contin. Dyn. Syst., Ser. S 14, No. 11, 3953-3971 (2021). Summary: An effective system of partial differential equations describing the heat and current flow through a thin organic light-emitting diode (OLED) mounted on a glass substrate is rigorously derived from a recently introduced fully three-dimensional \(p(x)\)-Laplace thermistor model. The OLED consists of several thin layers that scale differently with respect to the multiscale parameter \(\varepsilon>0\), which is the ratio between the total thickness and the lateral extent of the OLED. Starting point of the derivation is a rescaled formulation of the current-flow equation in the OLED for the driving potential and the heat equation in OLED and glass substrate with Joule heat term concentrated in the OLED. Assuming physically motivated scalings in the electrical flux functions, uniform a priori bounds are derived for the solutions of the three-dimensional system which facilitates the extraction of converging subsequences with limits that are identified as solutions of a dimension reduced system. In the latter, the effective current-flow equation is given by two semilinear equations in the two-dimensional cross-sections of the electrodes and algebraic equations for the continuity of the electrical fluxes through the organic layers. The effective heat equation is formulated only in the glass substrate with Joule heat term on the part of the boundary where the OLED is mounted. Cited in 3 Documents MSC: 35J92 Quasilinear elliptic equations with \(p\)-Laplacian 35Q79 PDEs in connection with classical thermodynamics and heat transfer 35J57 Boundary value problems for second-order elliptic systems 80A19 Diffusive and convective heat and mass transfer, heat flow 35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs 35B20 Perturbations in context of PDEs Keywords:thermistor system; joule heat; organic light-emitting diode; thin-film devices PDFBibTeX XMLCite \textit{A. Glitzky} et al., Discrete Contin. Dyn. Syst., Ser. S 14, No. 11, 3953--3971 (2021; Zbl 1481.35239) Full Text: DOI References: [1] E. Acerbi; G. Buttazzo; D. Percivale, A variational definition of the strain energy for an elastic string, J. Elasticity, 25, 137-148 (1991) · Zbl 0734.73094 [2] M. Bulíček; A. Glitzky; M. 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