Asymptotic modeling of the current flow system described by the p(x)$p(x)$‐Laplacian

Abstract Starting from the ‐Laplace thermistor model, in this paper we rigorously derive the effective model describing the current flow in a thin domain. We assume that the exponent is constant by parts and exhibiting the oscillating interface. Depending on the parameter describing these oscillations, we investigate the asymptotic behavior of the solution by using the adaptation of the periodic unfolding method. Our work is motivated by the industrial applications consisting of thin organic light‐emitting diodes.