Solution semigroup and invariant manifolds for functional equations with infinite delay

Hana Petzeltová

Mathematica Bohemica (1993)

  • Volume: 118, Issue: 2, page 175-193
  • ISSN: 0862-7959

Abstract

top
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.

How to cite

top

Petzeltová, Hana. "Solution semigroup and invariant manifolds for functional equations with infinite delay." Mathematica Bohemica 118.2 (1993): 175-193. <http://eudml.org/doc/29199>.

@article{Petzeltová1993,
abstract = {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.},
author = {Petzeltová, Hana},
journal = {Mathematica Bohemica},
keywords = {nonlinear diffusion-type equations with infinite delay; existence of stable and unstable manifolds; parabolic functional equation; infinite delay; stable and unstable manifolds; nonlinear diffusion-type equations with infinite delay; existence of stable and unstable manifolds},
language = {eng},
number = {2},
pages = {175-193},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Solution semigroup and invariant manifolds for functional equations with infinite delay},
url = {http://eudml.org/doc/29199},
volume = {118},
year = {1993},
}

TY - JOUR
AU - Petzeltová, Hana
TI - Solution semigroup and invariant manifolds for functional equations with infinite delay
JO - Mathematica Bohemica
PY - 1993
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 118
IS - 2
SP - 175
EP - 193
AB - 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.
LA - eng
KW - nonlinear diffusion-type equations with infinite delay; existence of stable and unstable manifolds; parabolic functional equation; infinite delay; stable and unstable manifolds; nonlinear diffusion-type equations with infinite delay; existence of stable and unstable manifolds
UR - http://eudml.org/doc/29199
ER -

References

top
  1. G. Da Prato A. Lunardi, 10.1007/BF00251457, Arch. Rat. Mech. Anal. 101 (1988), 115-141. (1988) MR0921935DOI10.1007/BF00251457
  2. G. Da Prato A. Lunardi, 10.1007/BF01761464, Ann. Mat. Pura Appl. 150 (1988), 67-117. (1988) MR0946030DOI10.1007/BF01761464
  3. J. K. Hale J. Kato, Phase space for retarded equations with infinite delay, Funkcial. Ekvac. 21 (1978), 11-41. (1978) MR0492721
  4. D. Henry, 10.1007/BFb0089647, Lecture Notes in Math., vol. 840, Springer Verlag, 1981. (1981) Zbl0456.35001MR0610244DOI10.1007/BFb0089647
  5. S. O. Londen J. A. Nohel, Nonlinear Volterra integrodifferential equation occuring in heat flow, J. Int. Equations 6(1984), 11-50. (1984) MR0727934
  6. A. Lunardi, 10.1002/mana.19851210120, Math. Nachr. 121 (1985), 295-318. (1985) Zbl0568.47035MR0809327DOI10.1002/mana.19851210120
  7. A. Lunardi, 10.1137/0521066, SIAM J. Math. Anal. 21 (1990), 1213-1224. (1990) MR1062400DOI10.1137/0521066
  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. (190,) MR1018887
  9. J. Milota, Stability and saddle-point property for a linear autonomous functional parabolic equations, Comm. Math. Univ. Carolinae 27 (1986), 87-101. (1986) MR0843423
  10. H. Petzeltová J. Milota, 10.1080/01630568708816261, Numer. Funct. Anal. and Optimiz. 9 (1987), 779-807. (1987) MR0910855DOI10.1080/01630568708816261
  11. E. Sinestrari, 10.1016/0022-247X(85)90353-1, J. Math. An. Appl. 107 (1985), 16-66. (1985) MR0786012DOI10.1016/0022-247X(85)90353-1
  12. C. C. Travis G. F. Webb, 10.1090/S0002-9947-1974-0382808-3, TAMS 200 (1974), 395-418. (1974) MR0382808DOI10.1090/S0002-9947-1974-0382808-3

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.