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Systems describing electrothermal effects with p(x)-Laplacian like structure for discontinuous variable exponents

Please always quote using this URN:urn:nbn:de:0296-matheon-13681
  • We consider a coupled system of two elliptic PDEs, where the elliptic term in the first equation shares the properties of the $p(x)$-Laplacian with discontinuous exponent, while in the second equation we have to deal with an a~priori $L^1$ term on the right hand side. Such a system of equations is suitable for the description of various electrothermal effects, in particular those, where the non-Ohmic behavior can change dramatically with respect to the spatial variable. We prove the existence of a weak solution under very weak assumptions on the data and also under general structural assumptions on the constitutive equations of the model. The main difficulty consists in the fact that we have to overcome simultaneously two obstacles - the discontinuous variable exponent (which limits the use of standard methods) and the $L^1$ right hand side of the heat equation. Our existence proof based on Galerkin approximation is highly constructive and therefore seems to be suitable also for numerical purposes.

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Metadaten
Author:Miroslav Bulíček, Annegret Glitzky, Matthias Liero
URN:urn:nbn:de:0296-matheon-13681
Referee:Frank Schmidt
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2016/02/04
Release Date:2016/02/04
Tag:Sobolev spaces with variable exponent, existence of weak solution, thermistor system, $p(x)-Laplacian, heat transfer
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 / 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:1099
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