Abstract
Consider the nonlinear parabolic system
$$\left\{\begin{array}{lll}
\frac{\partial b_i(x,u_i)}{\partial t}-\mathop{\rm
div}\Big(\mathcal{A}(x,t,u_i,\nabla u_i)+\Phi_i(x,t,u_i)\Big)+f_i(x,u_1,u_2)=
0 &\mbox{ in } Q_T \\ u_i=0 &\mbox{ on } \Gamma \\ b_i(x,u_i)(t=0)=b_i(x,u_{i,0})&\mbox{ in } \Omega,\end{array}\right.$$
where $ i=1,2$. In this paper we deal with the renormalized solution for the above system in Orlicz-Sobolev spaces where $f_i$ is a Carath\'{e}odory function satisfying some growth assumptions. The main term which contains the space derivatives and a non-coercive lower order term are considered in divergence form satisfying only the original Orlicz growths.
Key words: Parabolic systems; Orlicz growths; Orlicz-Sobolev spaces; renormalized solutions.
Full Text
Article Information
| Title | Existence result for some coupled nonlinear parabolic systems in Orlicz-Sobolev spaces |
| Source | Methods Funct. Anal. Topology, Vol. 31 (2025), no. 3, 172-194 |
| DOI | 10.31392/MFAT-npu26_3.2025.03 |
| Milestones | Received 21/09/2023; Revised 03/07/2025 |
| Copyright | The Author(s) 2025 (CC BY-SA) |
Authors Information
Jabir Ouazzani Chahdi
Department of Mathematics, Faculty of Sciences Tetouan, Abdelmalek Essaadi University, BP 2121, Tetouan, Morocco
Mohamed Bourahma
Laboratory LAMA, Department of mathematics, Faculty of Sciences Dhar el Mahraz, Sidi Mohamed Ben Abdellah University, PB 1796 Fez-Atlas, Fez, Morocco
Hassane Hjiaj
Department of Mathematics, Faculty of Sciences Tetouan, Abdelmalek Essaadi University, BP 2121, Tetouan, Morocco
Khalid Kaiba
Modeling and mathematical structures, Department of mathematics, Faculty of Sciences and technology of Fez, BOX 2202 Sidi Mohamed Ben Abdellah University, Fez, Morocco
Citation Example
Jabir Ouazzani Chahdi, Mohamed Bourahma, Hassane Hjiaj, and Khalid Kaiba, Existence result for some coupled nonlinear parabolic systems in Orlicz-Sobolev spaces, Methods Funct. Anal. Topology 31
(2025), no. 3, 172-194.
BibTex
@article {MFAT2123,
AUTHOR = {Jabir Ouazzani Chahdi and Mohamed Bourahma and Hassane Hjiaj and Khalid Kaiba},
TITLE = {Existence result for some coupled nonlinear parabolic systems in Orlicz-Sobolev spaces},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {31},
YEAR = {2025},
NUMBER = {3},
PAGES = {172-194},
ISSN = {1029-3531},
DOI = {10.31392/MFAT-npu26_3.2025.03},
URL = {https://mfat.imath.kiev.ua/article/?id=2123},
}
