Gallego, Francisco OrtegonRhoudaf, MohamedSabiki, Hajar2022-02-142022-02-142018-06-15Gallego, F. O., Rhoudaf, M., & Sabiki, H. (2018). Nonlinear parabolic-elliptic system in Musielak-Orlicz-Sobolev spaces. <i>Electronic Journal of Differential Equations, 2018</i>(121), pp. 1-36.1072-6691https://hdl.handle.net/10877/15321The existence of a capacity solution to the thermistor problem in the context of inhomogeneous Musielak-Orlicz-Sobolev spaces is analyzed. This is a coupled parabolic-elliptic system of nonlinear PDEs whose unknowns are the temperature inside a semiconductor material, u, and the electric potential, ϕ. We study the general case where the nonlinear elliptic operator in the parabolic equation is of the form Au = -div α(x, t, u, ∇u), A being a Leray-Lions operator defined on W1,x0 LM(QT), where M is a generalized N-function.Text37 pages1 file (.pdf)enAttribution 4.0 InternationalParabolic-elliptic systemMusielak-Orlicz-Sobolev spacesWeak solutionsCapacity solutionsArticle