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The generic behavior of solutions to some evolution equations: Asymptotics and Sobolev norms
Optimal regularity and stability analysis in the $\alpha$Norm for a class of partial functional differential equations with infinite delay
1.  Université Cadi Ayyad, Faculté des Sciences Semlalia, Département de Mathématiques, B.P.2390 Marrakech, Morocco 
2.  African Institute for Mathematical Sciences (AIMS), 6 Melrose Road, Muizenberg 7945, South Africa 
References:
[1] 
M. Adimy, A. Elazzouzi and K. Ezzinbi, Reduction principe and dynamic behaviors for a class of partial functional differential equations,, Nonlinear Analysis, 71 (2009), 1709. doi: 10.1016/j.na.2009.01.008. Google Scholar 
[2] 
R. Benkhalti and K. Ezzinbi, Existence and stability in the $\alpha$norm for some partial functinal differential equations with infinite delay,, Differential and Integral Equations, 19 (2006), 545. Google Scholar 
[3] 
O . Diekmann, S. A. Van Gils, S. M. Verduyn Lunel and H. O. walther, "Delay Equations, Functional, Complex and Nonlinear Analysis,", \textbf{110}, 110 (1995). Google Scholar 
[4] 
K. J. Engel and R. Nagel, "OneParameter Semigroups of Linear Evolution Equations,", \textbf{194}, 194 (2000). Google Scholar 
[5] 
K. Ezzinbi and A. Ouhinou, Necessary and sufficient conditions for the regularity and stability for some partial functional differential equations with infinite delay,, Nonlienar Analysis, 64 (2006), 1690. doi: 10.1016/j.na.2005.07.017. Google Scholar 
[6] 
K. Ezzinbi and A. Ouhinou, Stability and asymptotic behavior of solutions for some linear partial functional differential equations in critical cases,, Nonlienar Analysis, 70 (2009), 4008. doi: 10.1016/j.na.2008.08.010. Google Scholar 
[7] 
J. Hale and J. Kato, Phase space for retarded equations with unbounded delay,, Funkcial Ekvac, 21 (1978), 11. Google Scholar 
[8] 
Y. Hino, S. Murakami and T. Naito, "Functional Differential Equations with Infinite Delay,", \textbf{1473}, 1473 (1991). Google Scholar 
[9] 
T. Naito, J. S. Shin and S. Murakami, On solution semigroups of general functional differential equations,, Nonlinear Analysis, 30 (1997), 4565. doi: 10.1016/S0362546X(97)003155. Google Scholar 
[10] 
T. Naito, J. S. Shin and S. Murakami, On stability of solutions in linear autonomous functional differential equations,, Funkcialaj Ekvacioj, 43 (2000), 323. Google Scholar 
[11] 
T. Naito, J. S. Shin and S. Murakami, The generator of the solution semigroup for the general linear functional differential equation,, Bull. Univ.ElectroCommunications, 11 (1998), 29. Google Scholar 
[12] 
A. Pazy, "Semigroups of Linear Operators and Applications to Partial Differential Equations,", \textbf{44}, 44 (1983). Google Scholar 
[13] 
C. C. Travis and G. F. Webb, Partial differential equations with deviating arguments in the time variable,, Journal of Mathematical Analysis and Applications, 56 (1976), 397. doi: 10.1016/0022247X(76)900524. Google Scholar 
[14] 
C. C. Travis and G. F. Webb, Existence, stability and compactness in the $\alpha$norm for partial functional differential equations,, Transactions of the American Mathematical Society, 240 (1978), 129. doi: 10.2307/1998809. Google Scholar 
[15] 
J. Wu, "Theory and Applications of Partial Functional Differential Equations,", \textbf{119}, 119 (1996). Google Scholar 
show all references
References:
[1] 
M. Adimy, A. Elazzouzi and K. Ezzinbi, Reduction principe and dynamic behaviors for a class of partial functional differential equations,, Nonlinear Analysis, 71 (2009), 1709. doi: 10.1016/j.na.2009.01.008. Google Scholar 
[2] 
R. Benkhalti and K. Ezzinbi, Existence and stability in the $\alpha$norm for some partial functinal differential equations with infinite delay,, Differential and Integral Equations, 19 (2006), 545. Google Scholar 
[3] 
O . Diekmann, S. A. Van Gils, S. M. Verduyn Lunel and H. O. walther, "Delay Equations, Functional, Complex and Nonlinear Analysis,", \textbf{110}, 110 (1995). Google Scholar 
[4] 
K. J. Engel and R. Nagel, "OneParameter Semigroups of Linear Evolution Equations,", \textbf{194}, 194 (2000). Google Scholar 
[5] 
K. Ezzinbi and A. Ouhinou, Necessary and sufficient conditions for the regularity and stability for some partial functional differential equations with infinite delay,, Nonlienar Analysis, 64 (2006), 1690. doi: 10.1016/j.na.2005.07.017. Google Scholar 
[6] 
K. Ezzinbi and A. Ouhinou, Stability and asymptotic behavior of solutions for some linear partial functional differential equations in critical cases,, Nonlienar Analysis, 70 (2009), 4008. doi: 10.1016/j.na.2008.08.010. Google Scholar 
[7] 
J. Hale and J. Kato, Phase space for retarded equations with unbounded delay,, Funkcial Ekvac, 21 (1978), 11. Google Scholar 
[8] 
Y. Hino, S. Murakami and T. Naito, "Functional Differential Equations with Infinite Delay,", \textbf{1473}, 1473 (1991). Google Scholar 
[9] 
T. Naito, J. S. Shin and S. Murakami, On solution semigroups of general functional differential equations,, Nonlinear Analysis, 30 (1997), 4565. doi: 10.1016/S0362546X(97)003155. Google Scholar 
[10] 
T. Naito, J. S. Shin and S. Murakami, On stability of solutions in linear autonomous functional differential equations,, Funkcialaj Ekvacioj, 43 (2000), 323. Google Scholar 
[11] 
T. Naito, J. S. Shin and S. Murakami, The generator of the solution semigroup for the general linear functional differential equation,, Bull. Univ.ElectroCommunications, 11 (1998), 29. Google Scholar 
[12] 
A. Pazy, "Semigroups of Linear Operators and Applications to Partial Differential Equations,", \textbf{44}, 44 (1983). Google Scholar 
[13] 
C. C. Travis and G. F. Webb, Partial differential equations with deviating arguments in the time variable,, Journal of Mathematical Analysis and Applications, 56 (1976), 397. doi: 10.1016/0022247X(76)900524. Google Scholar 
[14] 
C. C. Travis and G. F. Webb, Existence, stability and compactness in the $\alpha$norm for partial functional differential equations,, Transactions of the American Mathematical Society, 240 (1978), 129. doi: 10.2307/1998809. Google Scholar 
[15] 
J. Wu, "Theory and Applications of Partial Functional Differential Equations,", \textbf{119}, 119 (1996). Google Scholar 
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