-
Previous Article
Existence and uniqueness of traveling waves in a class of unidirectional lattice differential equations
- DCDS Home
- This Issue
-
Next Article
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. |
[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.
|
[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).
|
[4] |
K. J. Engel and R. Nagel, "One-Parameter Semigroups of Linear Evolution Equations,", \textbf{194}, 194 (2000).
|
[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. |
[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. |
[7] |
J. Hale and J. Kato, Phase space for retarded equations with unbounded delay,, Funkcial Ekvac, 21 (1978), 11.
|
[8] |
Y. Hino, S. Murakami and T. Naito, "Functional Differential Equations with Infinite Delay,", \textbf{1473}, 1473 (1991).
|
[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/S0362-546X(97)00315-5. |
[10] |
T. Naito, J. S. Shin and S. Murakami, On stability of solutions in linear autonomous functional differential equations,, Funkcialaj Ekvacioj, 43 (2000), 323.
|
[11] |
T. Naito, J. S. Shin and S. Murakami, The generator of the solution semigroup for the general linear functional differential equation,, Bull. Univ.Electro-Communications, 11 (1998), 29.
|
[12] |
A. Pazy, "Semigroups of Linear Operators and Applications to Partial Differential Equations,", \textbf{44}, 44 (1983).
|
[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: 10.1016/0022-247X(76)90052-4. |
[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. |
[15] |
J. Wu, "Theory and Applications of Partial Functional Differential Equations,", \textbf{119}, 119 (1996).
|
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. |
[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.
|
[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).
|
[4] |
K. J. Engel and R. Nagel, "One-Parameter Semigroups of Linear Evolution Equations,", \textbf{194}, 194 (2000).
|
[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. |
[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. |
[7] |
J. Hale and J. Kato, Phase space for retarded equations with unbounded delay,, Funkcial Ekvac, 21 (1978), 11.
|
[8] |
Y. Hino, S. Murakami and T. Naito, "Functional Differential Equations with Infinite Delay,", \textbf{1473}, 1473 (1991).
|
[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/S0362-546X(97)00315-5. |
[10] |
T. Naito, J. S. Shin and S. Murakami, On stability of solutions in linear autonomous functional differential equations,, Funkcialaj Ekvacioj, 43 (2000), 323.
|
[11] |
T. Naito, J. S. Shin and S. Murakami, The generator of the solution semigroup for the general linear functional differential equation,, Bull. Univ.Electro-Communications, 11 (1998), 29.
|
[12] |
A. Pazy, "Semigroups of Linear Operators and Applications to Partial Differential Equations,", \textbf{44}, 44 (1983).
|
[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: 10.1016/0022-247X(76)90052-4. |
[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. |
[15] |
J. Wu, "Theory and Applications of Partial Functional Differential Equations,", \textbf{119}, 119 (1996).
|
[1] |
Giovambattista Amendola, Mauro Fabrizio, John Murrough Golden, Adele Manes. Energy stability for thermo-viscous fluids with a fading memory heat flux. Evolution Equations & Control Theory, 2015, 4 (3) : 265-279. doi: 10.3934/eect.2015.4.265 |
[2] |
Gary Froyland, Cecilia González-Tokman, Anthony Quas. Detecting isolated spectrum of transfer and Koopman operators with Fourier analytic tools. Journal of Computational Dynamics, 2014, 1 (2) : 249-278. doi: 10.3934/jcd.2014.1.249 |
[3] |
Aissa Guesmia, Nasser-eddine Tatar. Some well-posedness and stability results for abstract hyperbolic equations with infinite memory and distributed time delay. Communications on Pure & Applied Analysis, 2015, 14 (2) : 457-491. doi: 10.3934/cpaa.2015.14.457 |
[4] |
Yejuan Wang, Tongtong Liang. Mild solutions to the time fractional Navier-Stokes delay differential inclusions. Discrete & Continuous Dynamical Systems - B, 2019, 24 (8) : 3713-3740. doi: 10.3934/dcdsb.2018312 |
[5] |
Khalil Ezzinbi, James H. Liu, Nguyen Van Minh. Periodic solutions in fading memory spaces. Conference Publications, 2005, 2005 (Special) : 250-257. doi: 10.3934/proc.2005.2005.250 |
[6] |
Jin Liang, James H. Liu, Ti-Jun Xiao. Condensing operators and periodic solutions of infinite delay impulsive evolution equations. Discrete & Continuous Dynamical Systems - S, 2017, 10 (3) : 475-485. doi: 10.3934/dcdss.2017023 |
[7] |
Odo Diekmann, Karolína Korvasová. Linearization of solution operators for state-dependent delay equations: A simple example. Discrete & Continuous Dynamical Systems - A, 2016, 36 (1) : 137-149. doi: 10.3934/dcds.2016.36.137 |
[8] |
Cemil Tunç. Stability, boundedness and uniform boundedness of solutions of nonlinear delay differential equations. Conference Publications, 2011, 2011 (Special) : 1395-1403. doi: 10.3934/proc.2011.2011.1395 |
[9] |
Jiaohui Xu, Tomás Caraballo. Long time behavior of fractional impulsive stochastic differential equations with infinite delay. Discrete & Continuous Dynamical Systems - B, 2019, 24 (6) : 2719-2743. doi: 10.3934/dcdsb.2018272 |
[10] |
Arnaud Münch. A variational approach to approximate controls for system with essential spectrum: Application to membranal arch. Evolution Equations & Control Theory, 2013, 2 (1) : 119-151. doi: 10.3934/eect.2013.2.119 |
[11] |
C. Connell McCluskey. Global stability for an SEIR epidemiological model with varying infectivity and infinite delay. Mathematical Biosciences & Engineering, 2009, 6 (3) : 603-610. doi: 10.3934/mbe.2009.6.603 |
[12] |
Mansour Shrahili, Ravi Shanker Dubey, Ahmed Shafay. Inclusion of fading memory to Banister model of changes in physical condition. Discrete & Continuous Dynamical Systems - S, 2020, 13 (3) : 881-888. doi: 10.3934/dcdss.2020051 |
[13] |
Frédéric Naud. The Ruelle spectrum of generic transfer operators. Discrete & Continuous Dynamical Systems - A, 2012, 32 (7) : 2521-2531. doi: 10.3934/dcds.2012.32.2521 |
[14] |
Zhihua Liu, Pierre Magal. Functional differential equation with infinite delay in a space of exponentially bounded and uniformly continuous functions. Discrete & Continuous Dynamical Systems - B, 2017, 22 (11) : 0-0. doi: 10.3934/dcdsb.2019227 |
[15] |
István Győri, László Horváth. On the fundamental solution and its application in a large class of differential systems determined by Volterra type operators with delay. Discrete & Continuous Dynamical Systems - A, 2020, 40 (3) : 1665-1702. doi: 10.3934/dcds.2020089 |
[16] |
Robert T. Glassey, Walter A. Strauss. Perturbation of essential spectra of evolution operators and the Vlasov-Poisson-Boltzmann system. Discrete & Continuous Dynamical Systems - A, 1999, 5 (3) : 457-472. doi: 10.3934/dcds.1999.5.457 |
[17] |
Seung-Yeal Ha, Ho Lee, Seok Bae Yun. Uniform $L^p$-stability theory for the space-inhomogeneous Boltzmann equation with external forces. Discrete & Continuous Dynamical Systems - A, 2009, 24 (1) : 115-143. doi: 10.3934/dcds.2009.24.115 |
[18] |
Xin-Guang Yang, Jing Zhang, Shu Wang. Stability and dynamics of a weak viscoelastic system with memory and nonlinear time-varying delay. Discrete & Continuous Dynamical Systems - A, 2020, 40 (3) : 1493-1515. doi: 10.3934/dcds.2020084 |
[19] |
Hyeon Je Cho, Ganguk Hwang. Optimal design for dynamic spectrum access in cognitive radio networks under Rayleigh fading. Journal of Industrial & Management Optimization, 2012, 8 (4) : 821-840. doi: 10.3934/jimo.2012.8.821 |
[20] |
Frédéric Naud. Birkhoff cones, symbolic dynamics and spectrum of transfer operators. Discrete & Continuous Dynamical Systems - A, 2004, 11 (2&3) : 581-598. doi: 10.3934/dcds.2004.11.581 |
2018 Impact Factor: 1.143
Tools
Metrics
Other articles
by authors
[Back to Top]