Realization of any finite jet in a scalar semilinear parabolic equation on the ball in
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1991)
- Volume: 18, Issue: 1, page 83-102
- ISSN: 0391-173X
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topPoláčik, Peter. "Realization of any finite jet in a scalar semilinear parabolic equation on the ball in $\mathbb {R}^3$." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 18.1 (1991): 83-102. <http://eudml.org/doc/84097>.
@article{Poláčik1991,
author = {Poláčik, Peter},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {local dynamical system; dynamic complexity; restrictions; mode interaction bifurcation},
language = {eng},
number = {1},
pages = {83-102},
publisher = {Scuola normale superiore},
title = {Realization of any finite jet in a scalar semilinear parabolic equation on the ball in $\mathbb \{R\}^3$},
url = {http://eudml.org/doc/84097},
volume = {18},
year = {1991},
}
TY - JOUR
AU - Poláčik, Peter
TI - Realization of any finite jet in a scalar semilinear parabolic equation on the ball in $\mathbb {R}^3$
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1991
PB - Scuola normale superiore
VL - 18
IS - 1
SP - 83
EP - 102
LA - eng
KW - local dynamical system; dynamic complexity; restrictions; mode interaction bifurcation
UR - http://eudml.org/doc/84097
ER -
References
top- [Am] H. Amann, On abstract parabolic fundamental solutions, J. Math. Soc. Japan, 39 (1987), 93-116. Zbl0616.47032MR867989
- [Be] M.S. Berger, Nonlinearity and Functional Analysis, Academic Press, New York1977. Zbl0368.47001MR488101
- [Bi] Y.N. Bibikov, Bifurcation of invariant tori for systems with degeneracy, (in Russian), in: Questions of The Qualitative Theory of Differential Equations, V.M. Matrosov and L.Y. Anapolskii (eds.), Nauka, Novosibirsk1988, 1-23.
- [Ch-H] S.N. Chow - J.K. Hale, Methods of Bifurcation Theory, Springer-Verlag, New York1982. Zbl0487.47039MR660633
- [Co-H] R. Courant - D. Hilbert, Methods of Mathematical Physics, Interscience, New York1953. Zbl0051.28802MR65391
- [Da 1] E.N. Dancer, The effect of domain shape on the positive solutions of certain nonlinear equations, J. Differential Equations74 (1988), 120-156. Zbl0662.34025MR949628
- [Da 2] E.N. Dancer, On the existence of two-dimensional invariant tori for scalar parabolic equations with time periodic coefficients, preprint. Zbl0779.35049
- [F-P] B. Fiedler - P. POLÁčIK, Complicated dynamics of a scalar reaction diffusion equation with a nonlocal term, Proc. Roy. Soc. Edinburgh, 115A (1990), 167-192. Zbl0726.35060MR1059652
- [G-S] M. Golubitski - D. Schaeffer, Singularities and Groups in Bifurcation Theory, Appl. Math. Sci.51, Springer-Verlag, New York1986. Zbl0607.35004
- [Ha 1] J.K. Hale, Flows on centre manifolds for scalar functional differential equations, Proc. Roy. Soc. Edinburgh, 101A (1985), 193-201. Zbl0582.34058MR824220
- [Ha 2] J.K. Hale, Local flows for functional differential equations, Contemp. Math.56, Amer. Math. Soc., Providence1986, 185-192. Zbl0612.34066MR855090
- [He] D. Henry, Geometric Theory of Semilinear Parabolic Equations, Lecture Notes in Math., 840, Springer-Verlag, New York1981. Zbl0456.35001MR610244
- [Ka] T. Kato, Perturbation Theory for Linear Operators, Springer-Verlag, Berlin1966. Zbl0148.12601MR203473
- [Ma] H. Matano, Convergence of solutions of one-dimensional semilinear parabolic equations, J. Math. Kyoto Univ.18 (1978), 221-227. Zbl0387.35008MR501842
- [Po 1] P Poláčik, Convergence in smooth strongly monotone flows defined by semilinear parabolic equations, J. Differential Equations79 (1989), 89-110. Zbl0684.34064MR997611
- [Po 2] P Poláčik, Domains of attraction of equilibria and monotonicity properties of convergent trajectories in semilinear parabolic systems admitting strong comparison principle, J. Reine Angew. Math., 400 (1989), 32-56. Zbl0667.35036MR1013724
- [Po 3] P Poláčik, Complicated dynamics in scalar semilinear parabolic equations in higher space dimension, J. Differential Equations, 89 (1991), 244-271. Zbl0738.35027MR1091478
- [Po 4] P Poláčik, Imbedding of any vector field in a scalar semilinear parabolic equation, Proc. AMS, to appear. Zbl0755.35046MR1089411
- [Sm] V.I. Smirnov, A Course of Advanced Mathematics III2, Nauka, Moscow, 1974. MR361650
- [Ta] P Takáč, Domains of attraction of generic w-limit sets for strongly monotone semiflows, Z. Anal. Anwendungen, to appear. Zbl0764.58019MR1155611
- [Tr] H. Triebel, Interpolation Theory, Function Spaces, Differential Operators, North Holland, Amsterdam1978. Zbl0387.46032MR503903
- [Va] A. Vanderbauwhede, Local Bifurcation and Symmetry, Research Notes in Mathematics, Pitman, Boston1982. Zbl0539.58022MR697724
- [Ze] T.J. Zelenyak, Stabilization of solutions of boundary value problems for a second order parabolic equations with one space variable, Differential Equations4 (1968), pp. 17-22. Zbl0232.35053MR223758
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