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Keywords:
singularly perturbed evolution equations; C$^1$ stability of inertial manifolds
singularly perturbed evolution equations; C$^1$ stability of inertial manifolds
Summary:
In this paper we investigate the singular limiting behavior of slow invariant manifolds for a system of singularly perturbed evolution equations in Banach spaces. The aim is to prove the C$^{1}$ stability of invariant manifolds with respect to small values of the singular parameter.
References:
[1] Chow S.-N., Lu K.: Invariant manifolds for flows in Banach spaces. J. of Differential Equations 74 (1988), 285-317. MR 0952900 | Zbl 0691.58034
[2] Foias C., Sell G.R., Temam R.: Inertial manifolds for nonlinear evolutionary equations. J. of Differential Equations 73 (1988), 309-353. MR 0943945 | Zbl 0643.58004
[3] Henry D.: Geometric theory of semilinear parabolic equations. Lecture Notes in Math. 840, Springer Verlag, 1981. MR 0610244 | Zbl 0663.35001
[4] Marion M.: Inertial manifolds associated to partly dissipative reaction - diffusion systems. J. of Math. Anal. Appl. 143 (1989), 295-326. MR 1022538 | Zbl 0689.58039
[5] Miklavčič M.: A sharp condition for existence of an inertial manifold. J. of Dynamics and Differential Equations 3 (1991), 437-457. MR 1118343
[6] Mora X., Solà-Morales J.: The singular limit dynamics of semilinear damped wave equation. J. of Differential Equations 78 (1989), 262-307. MR 0992148
[7] Richards J.: On the gaps between numbers which are the sum of two squares. Adv. Math. 46 (1982), 1-2. MR 0676985
[8] Ševčovič D.: Limiting behaviour of invariant manifolds for a system of singularly perturbed evolution equations. Math. Methods in the Appl. Sci. 17 (1994), 643-666. MR 1280649
[9] Ševčovič D.: Limiting behavior of global attractors for singularly perturbed beam equations with strong damping. Comment. Math. Univ. Carolinae 32 (1991), 45-60. MR 1118289
[10] Sviridyuk G.A.: The Deborah number and a class of semilinear equations of Sobolev type (English translation). Soviet. Math. Doklady 44 No.1 (1992), 297-301. MR 1152892
[11] Sviridyuk G.A., Sukacheva T.G.: Cauchy problem for a class of semilinear equations of Sobolev type (English translation). Sibirskii Matem. Zhurnal 31 No.5 (1990), 120-127. MR 1088921
[12] Vanderbauwhede A., Van Gils V.A.: Center manifolds and contraction on a scale of Banach spaces. J. of Funct. Analysis 72 (1987), 209-224. MR 0886811
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