| Title:
|
The C$^1$ stability of slow manifolds for a system of singularly perturbed evolution equations (English) |
| Author:
|
Ševčovič, Daniel |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
36 |
| Issue:
|
1 |
| Year:
|
1995 |
| Pages:
|
89-107 |
| . |
| Category:
|
math |
| . |
| 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. (English) |
| Keyword:
|
singularly perturbed evolution equations |
| Keyword:
|
C$^1$ stability of inertial manifolds |
| MSC:
|
34D45 |
| MSC:
|
34E15 |
| MSC:
|
34G20 |
| MSC:
|
35B25 |
| MSC:
|
35B40 |
| MSC:
|
35C30 |
| MSC:
|
35K55 |
| MSC:
|
35L15 |
| MSC:
|
47H20 |
| idZBL:
|
Zbl 0821.35011 |
| idMR:
|
MR1334417 |
| . |
| Date available:
|
2009-01-08T18:16:14Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118735 |
| . |
| Reference:
|
[1] Chow S.-N., Lu K.: Invariant manifolds for flows in Banach spaces.J. of Differential Equations 74 (1988), 285-317. Zbl 0691.58034, MR 0952900 |
| Reference:
|
[2] Foias C., Sell G.R., Temam R.: Inertial manifolds for nonlinear evolutionary equations.J. of Differential Equations 73 (1988), 309-353. Zbl 0643.58004, MR 0943945 |
| Reference:
|
[3] Henry D.: Geometric theory of semilinear parabolic equations.Lecture Notes in Math. 840, Springer Verlag, 1981. Zbl 0663.35001, MR 0610244 |
| Reference:
|
[4] Marion M.: Inertial manifolds associated to partly dissipative reaction - diffusion systems.J. of Math. Anal. Appl. 143 (1989), 295-326. Zbl 0689.58039, MR 1022538 |
| Reference:
|
[5] Miklavčič M.: A sharp condition for existence of an inertial manifold.J. of Dynamics and Differential Equations 3 (1991), 437-457. MR 1118343 |
| Reference:
|
[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 |
| Reference:
|
[7] Richards J.: On the gaps between numbers which are the sum of two squares.Adv. Math. 46 (1982), 1-2. MR 0676985 |
| Reference:
|
[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 |
| Reference:
|
[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 |
| Reference:
|
[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 |
| Reference:
|
[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 |
| Reference:
|
[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 |
| . |
