Electron. J. Differential Equations, Vol. 2023 (2023), No. 39, pp. 1-17.

Reduction principle for partial functional differential equation without compactness

Meryem El Attaouy, Khalil Ezzinbi, Gaston Mandata N'Guerekata

Abstract:
This article establishes a reduction principle for partial functional differential equation without compactness of the semigroup generated by the linear part. Under conditions more general than the compactness of the C0-semigroup generated by the linear part, we establish the quasi-compactness of the C0-semigroup associated to the linear part of the partial functional differential equation. This result allows as to construct a reduced system that is posed by an ordinary differential equation posed in a finite dimensional space. Through this result we study the existence of almost automorphic and almost periodic solutions for partial functional differential equations. For illustration, we study a transport model.

Submitted May 23, 2022. Published June 20, 2023.
Math Subject Classifications: 35G15, 35G20, 35G25, 35G30.
Key Words: Functional differential equations; quasi-compact semigroup;
DOI: https://doi.org/10.58997/ejde.2023.39

variation of constants formula; Stepanov-almost automorphic function; almost automorphic solution; almost periodic solution.

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Meryem El Attaouy
Cadi Ayyad University
Faculty of Science Semlalia
Department of Mathematics
BP 2390 Marrakech, Morocco
email: meryemelattaouy@gmail.com
Khalil Ezzinbi
Cadi Ayyad University
Faculty of Science Semlalia
Department of Mathematics
BP 2390 Marrakech, Morocco
email: ezzinbi@uca.ac.ma
Gaston Mandata N'Guérékata
NEERLab, Department of Mathematics
Morgan State University Baltimore, MD 21251, USA
email: gaston.nguerekata@morgan.edu

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