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Shape stability of optimal control problems in coefficients for coupled system of Hammerstein type
Invariant stable manifolds for partial neutral functional differential equations in admissible spaces on a half-line
1. | School of Applied Mathematics and Informatics, Hanoi University of Science and Technology, 1 Dai Co Viet, Hanoi, Vietnam |
2. | Department of Basic Sciences, University of Economic and Technical Industries, 456-Minh Khai Str., Hai Ba Trung, Hanoi, Vietnam |
References:
[1] |
B. Aulbach and N. V. Minh, Nonlinear semigroups and the existence and stability of semilinear nonautonomous evolution equations, Abstr. Appl. Anal., 1 (1996), 351-380.
doi: 10.1155/S108533759600019X. |
[2] |
P. Bates and C. Jones, Invariant manifolds for semilinear partial differential equations, Dyn. Rep., 2 (1989), 1-38. |
[3] |
R. Benkhalti, K. Ezzinbi and S. Fatajou, Stable and unstable manifolds for nonlinear partial neutral functional differential equations, Diff. Integr. Eq., 23 (2010), 773-794. |
[4] |
L. Boutet de Monvel, I. D. Chueshov and A. V. Rezounenko, Inertial manifolds for retarded semilinear parabolic equations, Nonlinear Analysis, 34 (1998), 907-925.
doi: 10.1016/S0362-546X(97)00569-5. |
[5] |
J. Carr, Applications of Centre Manifold Theory, Applied Mathematical Sciences 35, Springer-Verlag, New York-Berlin, 1981. |
[6] |
C. Chicone, Ordinary Differential Equations with Applications, Springer-Verlag, 1999. |
[7] |
I. D. Chueshov and M. Scheutzow, Inertial manifolds and forms for stochastically perturbed retarded semilinear parabolic equations, Journal of Dynamics and Differential Equations, 13 (2001), 355-380.
doi: 10.1023/A:1016684108862. |
[8] |
K. J. Engel and R. Nagel, One-parameter Semigroups for Linear Evolution Equations, Graduate Text Math. 194, Springer-Verlag, New York, 2000. |
[9] |
N. T. Huy, Stable manifolds for semi-linear evolution equations and admissibility of function spaces on a half-line, J. Math. Anal. Appl., 354 (2009), 372-386.
doi: 10.1016/j.jmaa.2008.12.062. |
[10] |
N. T. Huy, Exponential dichotomy of evolution equations and admissibility of function spaces on a half-line, J. Funct. Anal., 235 (2006), 330-354.
doi: 10.1016/j.jfa.2005.11.002. |
[11] |
N. T. Huy and T. V. Duoc, Integral manifolds for partial functional differential equations in admissible spaces on a half-line, Journal of Mathematical Analysis and Applications, 411 (2014), 816-828.
doi: 10.1016/j.jmaa.2013.10.027. |
[12] |
R. Martin, Nonlinear Operators and Differential Equations in Banach Spaces, Wiley Interscience, New York, 1976. |
[13] |
J. L. Massera and J. J. Schäffer, Linear Differential Equations and Function Spaces, Academic Press, New York, 1966. |
[14] |
N. V. Minh, F. Räbiger and R. Schnaubelt, Exponential stability, exponential expansiveness and exponential dichotomy of evolution equations on the half line, Integral Equations Operator Theory, 32 (1998), 332-353.
doi: 10.1007/BF01203774. |
[15] |
N. V. Minh and J. Wu, Invariant manifolds of partial functional differential equations, J. Differential Equations, 198 (2004), 381-421.
doi: 10.1016/j.jde.2003.10.006. |
[16] |
J. D. Murray, Mathematical Biology I: An Introduction, Springer-Verlag, New York, 2002. |
[17] |
J. D. Murray, Mathematical Biology II: Spatial Models and Biomedical Applications, Springer-Verlag, New York, 2003. |
[18] |
R. Nagel and G. Nickel, Well-posedness for non-autonomous abstract Cauchy problems, Progr. Nonlinear Differential Equations Appl., 50 (2002), 279-293. |
[19] |
A. Pazy, Semigroup of Linear Operators and Application to Partial Differential Equations, Springer-Verlag, Berlin, 1983.
doi: 10.1007/978-1-4612-5561-1. |
[20] |
H. Petzeltová and O. J. Staffans, Spectral decomposition and invariant manifolds for some functional partial differential equations, J. Diff. Eq., 138 (1997), 301-327.
doi: 10.1006/jdeq.1997.3277. |
[21] |
F. Räbiger and R. Schnaubelt, The spectral mapping theorem for evolution semigroups on spaces of vector-valued functions, Semigroup Forum, 52 (1996), 225-239.
doi: 10.1007/BF02574098. |
[22] |
H. Triebel, Interpolation Theory, Function Spaces, Differential Operators, North-Holland, Amsterdam, New York, Oxford, 1978. |
[23] |
J. Wu, Theory and Applications of Partial Functional Differential Equations, Springer Verlag, New York, 1996.
doi: 10.1007/978-1-4612-4050-1. |
[24] |
A. Yagi, Abstract Parabolic Evolution Equations and their Applications, Springer-Verlag, Berlin, 2010.
doi: 10.1007/978-3-642-04631-5. |
show all references
References:
[1] |
B. Aulbach and N. V. Minh, Nonlinear semigroups and the existence and stability of semilinear nonautonomous evolution equations, Abstr. Appl. Anal., 1 (1996), 351-380.
doi: 10.1155/S108533759600019X. |
[2] |
P. Bates and C. Jones, Invariant manifolds for semilinear partial differential equations, Dyn. Rep., 2 (1989), 1-38. |
[3] |
R. Benkhalti, K. Ezzinbi and S. Fatajou, Stable and unstable manifolds for nonlinear partial neutral functional differential equations, Diff. Integr. Eq., 23 (2010), 773-794. |
[4] |
L. Boutet de Monvel, I. D. Chueshov and A. V. Rezounenko, Inertial manifolds for retarded semilinear parabolic equations, Nonlinear Analysis, 34 (1998), 907-925.
doi: 10.1016/S0362-546X(97)00569-5. |
[5] |
J. Carr, Applications of Centre Manifold Theory, Applied Mathematical Sciences 35, Springer-Verlag, New York-Berlin, 1981. |
[6] |
C. Chicone, Ordinary Differential Equations with Applications, Springer-Verlag, 1999. |
[7] |
I. D. Chueshov and M. Scheutzow, Inertial manifolds and forms for stochastically perturbed retarded semilinear parabolic equations, Journal of Dynamics and Differential Equations, 13 (2001), 355-380.
doi: 10.1023/A:1016684108862. |
[8] |
K. J. Engel and R. Nagel, One-parameter Semigroups for Linear Evolution Equations, Graduate Text Math. 194, Springer-Verlag, New York, 2000. |
[9] |
N. T. Huy, Stable manifolds for semi-linear evolution equations and admissibility of function spaces on a half-line, J. Math. Anal. Appl., 354 (2009), 372-386.
doi: 10.1016/j.jmaa.2008.12.062. |
[10] |
N. T. Huy, Exponential dichotomy of evolution equations and admissibility of function spaces on a half-line, J. Funct. Anal., 235 (2006), 330-354.
doi: 10.1016/j.jfa.2005.11.002. |
[11] |
N. T. Huy and T. V. Duoc, Integral manifolds for partial functional differential equations in admissible spaces on a half-line, Journal of Mathematical Analysis and Applications, 411 (2014), 816-828.
doi: 10.1016/j.jmaa.2013.10.027. |
[12] |
R. Martin, Nonlinear Operators and Differential Equations in Banach Spaces, Wiley Interscience, New York, 1976. |
[13] |
J. L. Massera and J. J. Schäffer, Linear Differential Equations and Function Spaces, Academic Press, New York, 1966. |
[14] |
N. V. Minh, F. Räbiger and R. Schnaubelt, Exponential stability, exponential expansiveness and exponential dichotomy of evolution equations on the half line, Integral Equations Operator Theory, 32 (1998), 332-353.
doi: 10.1007/BF01203774. |
[15] |
N. V. Minh and J. Wu, Invariant manifolds of partial functional differential equations, J. Differential Equations, 198 (2004), 381-421.
doi: 10.1016/j.jde.2003.10.006. |
[16] |
J. D. Murray, Mathematical Biology I: An Introduction, Springer-Verlag, New York, 2002. |
[17] |
J. D. Murray, Mathematical Biology II: Spatial Models and Biomedical Applications, Springer-Verlag, New York, 2003. |
[18] |
R. Nagel and G. Nickel, Well-posedness for non-autonomous abstract Cauchy problems, Progr. Nonlinear Differential Equations Appl., 50 (2002), 279-293. |
[19] |
A. Pazy, Semigroup of Linear Operators and Application to Partial Differential Equations, Springer-Verlag, Berlin, 1983.
doi: 10.1007/978-1-4612-5561-1. |
[20] |
H. Petzeltová and O. J. Staffans, Spectral decomposition and invariant manifolds for some functional partial differential equations, J. Diff. Eq., 138 (1997), 301-327.
doi: 10.1006/jdeq.1997.3277. |
[21] |
F. Räbiger and R. Schnaubelt, The spectral mapping theorem for evolution semigroups on spaces of vector-valued functions, Semigroup Forum, 52 (1996), 225-239.
doi: 10.1007/BF02574098. |
[22] |
H. Triebel, Interpolation Theory, Function Spaces, Differential Operators, North-Holland, Amsterdam, New York, Oxford, 1978. |
[23] |
J. Wu, Theory and Applications of Partial Functional Differential Equations, Springer Verlag, New York, 1996.
doi: 10.1007/978-1-4612-4050-1. |
[24] |
A. Yagi, Abstract Parabolic Evolution Equations and their Applications, Springer-Verlag, Berlin, 2010.
doi: 10.1007/978-3-642-04631-5. |
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