Abstract
This paper is concerned with the existence and the uniqueness of weak periodic solution for the following nonlinear parabolic–elliptic problem \(\frac{\partial u}{\partial t}-{\text {div}}({\mathcal {H}}(x,t,u,\nabla u))+\kappa (u)\beta ^{\prime }(u)\nabla u\nabla v=\kappa (u)|\nabla v|^{2}\) and \(\hbox {div}(\kappa (u)\nabla v)=0\) in Orlicz–Sobolev spaces, equipped with a specific N-functions. The proof is based on the theoretical frameworks of maximal monotonic maps and Schauder’s fixed point theorem.
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Ahakkoud, Y., Bennouna, J. & Elmassoudi, M. Weak periodic solutions of a parabolic–elliptic system with Joule–Thomson effect. Bol. Soc. Mat. Mex. 29, 67 (2023). https://doi.org/10.1007/s40590-023-00539-7
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DOI: https://doi.org/10.1007/s40590-023-00539-7
Keywords
- Periodic solution
- Weak solution
- Coupled system
- Leray–Schauder theorem
- Orlicz–Sobolev spaces
- Joule–Thomson effect