Stability and local attractivity for non-autonomous boundary Cauchy problems
Abstract
In this paper we present results concerning the existence, stability and local attractivity for non-autonomous semilinear boundary Cauchy problems. In our method, we assume certain smoothness properties on the linear part and the local lipshitz continuity on the nonlinear perturbation. We apply our abstract results to population equations.
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References
T. Akrid, L. Maniar, and A. Ouhinou, Periodic Solutions of Nondensely Nonautonomous Differential Equations with Delay, Afr. Diaspora J. Math. (N.S.), Volume 15, Number 1 (2013), 25-42.
J. Blot, C. Buse and P. Cieutat, Local attractivity in nonautonomous semilinear evolution equations, Nonauton. Dyn. Syst., Volume 1, Number 1 (2014), 72-82. https://doi.org/10.2478/msds-2014-0002 DOI: https://doi.org/10.2478/msds-2014-0002
S. Boulite, A. Idrissi and L. Maniar, Controllability of semi-linear boundary problems with nonlocal initial conditions, Journal of Mathematical Analysis and Applications, Volume 316, Number 1 (2006), 566-578. https://doi.org/10.1016/j.jmaa.2005.05.006 DOI: https://doi.org/10.1016/j.jmaa.2005.05.006
S. Boulite, L. Maniar and M. Moussi, Wellposedness and asymptotic behaviour of nonautonomous boundary Cauchy problems, Forum Mathematicum, Volume 18, Number 4 (2006), 611-638. https://doi.org/10.1515/FORUM.2006.032 DOI: https://doi.org/10.1515/FORUM.2006.032
T. S. Doan, Moussi and S. Siegmund, Integral manifolds of nonautonomous boundary Cauchy problem, Journal of Nonlinear Evolution Equations and Applications, Volume 2012, Number 1 (2012), 1-15.
G. Greiner, Perturbing the boundary conditions of a generator, Houston Journal of Mathematics, Volume 13, Number 2 (1987), 213-229.
N. T. Lan, Non-autonomous operator matrices, Ph.D. thesis, Tubingen university, 1998.
M. Moussi, Well-posdness and asymptotic behavior of non-autonomous boundary Cauchy problems, Ph.D. thesis, Faculty of science, Oujda, 2003.
M. Moussi, Pullback attractors of Nonautonomous Boundary Cauchy Problems, Nonlinear Dynamics and Systems Theory, Volume 14, Number 4 (2014), 383-394.
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