| Title:
|
Local center manifold for parabolic equations with infinite delay (English) |
| Author:
|
Petzeltová, Hana |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
119 |
| Issue:
|
3 |
| Year:
|
1994 |
| Pages:
|
285-304 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The existence and attractivity of a local center manifold for fully nonlinear parabolic equation with infinite delay is proved with help of a solutions semigroup constructed on the space of initial conditions. The result is applied to the stability problem for a parabolic integrodifferential equation. (English) |
| Keyword:
|
parabolic integrodifferential equations |
| Keyword:
|
invariant manifolds |
| Keyword:
|
functional equations |
| Keyword:
|
analytic semigroup |
| Keyword:
|
Banach space |
| Keyword:
|
resolvent operator |
| Keyword:
|
interpolation spaces |
| Keyword:
|
center manifold |
| Keyword:
|
parabolic functional equation |
| Keyword:
|
infinite delay |
| Keyword:
|
solution semigroup |
| MSC:
|
34K15 |
| MSC:
|
34K20 |
| MSC:
|
34K30 |
| MSC:
|
35B35 |
| MSC:
|
35R10 |
| MSC:
|
45K05 |
| MSC:
|
45N05 |
| MSC:
|
47N20 |
| idZBL:
|
Zbl 0818.45005 |
| idMR:
|
MR1305531 |
| DOI:
|
10.21136/MB.1994.126163 |
| . |
| Date available:
|
2009-09-24T21:06:08Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/126163 |
| . |
| Reference:
|
[1] P. Acquistаpаce B. Tereni: Hölder classes with boundaгy conditions as interpolation spaces.Math Z. 195 (1987), 451-471. MR 0900340 |
| Reference:
|
[2] G. Dа Prаto A. Lunаrdi: Stability, instability and center manifold theorem for fully nonlinear autonomous parabolic equations in Banach space.Arch. Rat. Mech. Anal. 101 (1988), 115-141. MR 0921935, 10.1007/BF00251457 |
| Reference:
|
[3] J. K. Hаle J. Kаto: Phase space for retarded equations with infinite delay.Funkcial. Ekvac. 21 (1978), 11-41. MR 0492721 |
| Reference:
|
[4] D. Henry: Geometric theory of semilinear parabolic equations.Lecture Notes in Math. 840, Springer Verlag, 1981. Zbl 0456.35001, MR 0610244, 10.1007/BFb0089647 |
| Reference:
|
[5] S. O. Londen J. A. Nohel: Nonlinear Volterra integrodifferential equation occuring in heat flow.Ј. Int. Equations 6 (1984), 11-50. MR 0727934 |
| Reference:
|
[6] A. Lunаrdi: Interpolation spaces between domains of elliptic operators and spaces of continuous functions with applications to nonlinear parabolic equations.Math. Nachr. 121 (1985), 295-318. MR 0809327, 10.1002/mana.19851210120 |
| Reference:
|
[7] A. Lunаrdi: Stability and local invariant manifolds in fully nonlinear parabolic equations.Preprint. MR 1270699 |
| Reference:
|
[8] J. Milotа: Asymptotic behaviour of parabolic equations with infinite delay.Volterra Integrodiff. Eqs. and Appl., Pitman Research Notes in Math. 190 (1989), 295-305. MR 1018887 |
| Reference:
|
[9] H. Petzeltová: Solution semigroup and invariant manifolds for functional equations with infìnite delay.Mathematica Bohemica 118 (1993), no. 2, 175-193. MR 1223484 |
| Reference:
|
[10] H. Petzeltová J. Milotа: Resolvent operator for abstract functional differential equations with infinite delay.Numer. Funct. Anal. and Optimiz. 9 (1987), 779-807. 10.1080/01630568708816261 |
| Reference:
|
[11] G. Simonett: Zentrumsmannigfaltigkeiten für quasilineare parabolische Gleichungen.Thesis. |
| Reference:
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[12] E. Sinestrаri: On the abstract Cauchy problem of parabolic type in the spaces of continuous functions.Ј. Math. And Appl. 107(1985), 16-66. |
| Reference:
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[13] A. Vаnderbаuwhede: Center manifolds, normal forms and elementary bifurcations.Dynamics reported 2 (1989), 89-169. MR 1000977, 10.1007/978-3-322-96657-5_4 |
| Reference:
|
[14] A. Vanderbauwhede G. Iooss: Center manifold theory in infìnite dimensions.Dynamics reported 1 (1992), 125-163. MR 1153030, 10.1007/978-3-642-61243-5_4 |
| . |
