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