Nonlinear parabolic-elliptic system in Musielak-Orlicz-Sobolev spaces

Date

2018-06-15

Authors

Gallego, Francisco Ortegon
Rhoudaf, Mohamed
Sabiki, Hajar

Journal Title

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Volume Title

Publisher

Texas State University, Department of Mathematics

Abstract

The 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.

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Keywords

Parabolic-elliptic system, Musielak-Orlicz-Sobolev spaces, Weak solutions, Capacity solutions

Citation

Gallego, 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.

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Attribution 4.0 International

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