Systems describing electrothermal effects with \(p(x)\)-Laplacian-like structure for discontinuous variable exponents (Q2827750)

The authors consider a system of two elliptic equations accompanied by certain Dirichlet, Neumann, and Newton boundary conditions. In the first equation the growth condition for the elliptic term depends on the spatial variable, and the second one has a right-hand side in \(L^1\). This kind of systems can model various electrothermal effects, such as self-heating and inhomogeneous current distributions, in organic, i.e., carbon-based, semiconductor devices and in particular, those where the non-Ohmic behavior can change strongly with respect to the spatial variable. As a main result, the authors prove the existence of a weak solution under weak assumptions on the data and also under general structural assumptions on the constitutive equations of the model. In the last of the paper there are given a physical example of a model for the electrothermal behavior of organic light-emitting diodes that fits into the assumptions of the main result of the paper.