TY - GEN A1 - Bulicek, Miroslav A1 - Glitzky, Annegret A1 - Liero, Matthias T1 - Thermistor systems of p(x)-Laplace type with discontinuous exponents via entropy solutions N2 - We show the existence of solutions to a system of elliptic PDEs, that was recently introduced to describe the electrothermal behavior of organic semiconductor devices. Here, two diffculties appear: (i) the elliptic term in the current-flow equation is of p(x)-Laplacian type with discontinuous exponent p, which limits the use of standard methods, and (ii) in the heat equation, we have to deal with an a priori L1 term on the right hand side describing the Joule heating in the device. We prove the existence of a weak solution under very weak assumptions on the data. Our existence proof is based on Schauder’s fixed point theorem and the concept of entropy solutions for the heat equation. Here, the crucial point is the continuous dependence of the entropy solutions on the data of the problem. KW - Sobolev spaces with variable exponent KW - existence of weak solution KW - entropy solution KW - thermistor system KW - p(x)-Laplacian KW - heat transfer Y1 - 2016 UR - https://opus4.kobv.de/opus4-matheon/frontdoor/index/index/docId/1396 UR - https://nbn-resolving.org/urn:nbn:de:0296-matheon-13962 ER -