Stability and asymptotic behavior of solutions for some linear partial functional differential equations in critical cases |
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Authors: | Khalil Ezzinbi Aziz Ouhinou |
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Institution: | Université Cadi Ayyad, Faculté des Sciences Semlalia, Département de Mathématiques, B.P. 2390, Marrakesh, Morocco |
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Abstract: | In this work, we study the stability of the solution semigroup for some linear partial functional differential equations with infinite delay in a Banach space when the exponential stability fails. We use the so-called characteristic equation to compute the order of each pole of the resolvent operator associated with the infinitesimal generator of the solution semigroup. This result allows us to give sufficient conditions for having stability of the solution semigroup. |
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Keywords: | Hille&ndash Yosida operator Uniform fading memory space Semigroup solution Infinitesimal generator Characteristic equation Essential spectrum Stability |
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