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Existence and Uniqueness Results for Quasilinear Parabolic Systems in Orlicz Spaces

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Abstract

We establish an existence and uniqueness result for quasilinear parabolic systems of the form \(\frac {\partial u}{\partial t}-\text {div} \sigma (x,t,Du)=f\) in Q, where the source term f is assumed to be in \(W^{-1,x}E_{\overline {M}}(Q;\mathbb {R}^{m})\). The proof is based on the theory of Young measures which permits to identify weak limits.

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Acknowledgements

The authors would like to thank the referees for constructive suggestions which help us in depth to improve the quality of the paper.

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  1. Faculty of Sciences Dhar El Mehraz, B.P. 1796, Atlas, Fez, Morocco

    Farah Balaadich & Elhoussine Azroul

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  1. Farah Balaadich
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  2. Elhoussine Azroul
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Correspondence to Farah Balaadich.

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Balaadich, F., Azroul, E. Existence and Uniqueness Results for Quasilinear Parabolic Systems in Orlicz Spaces. J Dyn Control Syst 26, 407–421 (2020). https://doi.org/10.1007/s10883-019-09447-4

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  • DOI: https://doi.org/10.1007/s10883-019-09447-4

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