| Title:
|
Solution semigroup and invariant manifolds for functional equations with infinite delay (English) |
| Author:
|
Petzeltová, Hana |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
118 |
| Issue:
|
2 |
| Year:
|
1993 |
| Pages:
|
175-193 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
It is proved that parabolic equations with infinite delay generate $C_0$-semigroup on the space of initial conditions, such that local stable and unstable manifolds can be constructed for a fully nonlinear problems with help of usual methods of the theory of parabolic equations. (English) |
| Keyword:
|
nonlinear diffusion-type equations with infinite delay |
| Keyword:
|
existence of stable and unstable manifolds |
| Keyword:
|
parabolic functional equation |
| Keyword:
|
infinite delay |
| Keyword:
|
stable and unstable manifolds |
| MSC:
|
34K30 |
| MSC:
|
34K99 |
| MSC:
|
35B35 |
| MSC:
|
35B40 |
| MSC:
|
35R10 |
| MSC:
|
45K05 |
| MSC:
|
47D06 |
| MSC:
|
47N20 |
| idZBL:
|
Zbl 0798.35153 |
| idMR:
|
MR1223484 |
| DOI:
|
10.21136/MB.1993.126045 |
| . |
| Date available:
|
2009-09-24T20:58:44Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/126045 |
| . |
| Reference:
|
[1] G. Da Prato A. Lunardi: 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:
|
[2] G. Da Prato A. Lunardi: Solvability on the real line of a class of linear Volterra integrodifferential equations of parabolic type.Ann. Mat. Pura Appl. 150 (1988), 67-117. MR 0946030, 10.1007/BF01761464 |
| Reference:
|
[3] J. K. Hale J. Kato: 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., vol. 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.J. Int. Equations 6(1984), 11-50. MR 0727934 |
| Reference:
|
[6] A. Lunardi: Interpolation spaces between domains of elliptic operators and spaces of continuous functions with applications to nonlinear parabolic equations.Math. Nachr. 121 (1985), 295-318. Zbl 0568.47035, MR 0809327, 10.1002/mana.19851210120 |
| Reference:
|
[7] A. Lunardi: On the linear heat equation for materials of fading memory type.SIAM J. Math. Anal. 21 (1990), 1213-1224. MR 1062400, 10.1137/0521066 |
| Reference:
|
[8] J. Milota: Asymptotic behaviour of parabolic equations with infinite delay.Volterra Integrodiff. Eqs. and Appl., Pitman Research Notes in Math. 190, 1989, pp. 295-305. MR 1018887 |
| Reference:
|
[9] J. Milota: Stability and saddle-point property for a linear autonomous functional parabolic equations.Comm. Math. Univ. Carolinae 27 (1986), 87-101. MR 0843423 |
| Reference:
|
[10] H. Petzeltová J. Milota: Resolvent operator for abstract functional differential equations with infinite delay.Numer. Funct. Anal. and Optimiz. 9 (1987), 779-807. MR 0910855, 10.1080/01630568708816261 |
| Reference:
|
[11] E. Sinestrari: On the abstract Cauchy problem of parabolic type in the spaces of continuous functions.J. Math. An. Appl. 107 (1985), 16-66. MR 0786012, 10.1016/0022-247X(85)90353-1 |
| Reference:
|
[12] C. C. Travis G. F. Webb: Existence and stability for partial functional differential equations.TAMS 200 (1974), 395-418. MR 0382808, 10.1090/S0002-9947-1974-0382808-3 |
| . |
