Realization of any finite jet in a scalar semilinear parabolic equation on the ball in ℝ 3
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 18 (1991) no. 1, pp. 83-102. 
@article{ASNSP_1991_4_18_1_83_0,
     author = {Pol\'a\v{c}ik, Peter},
     title = {Realization of any finite jet in a scalar semilinear parabolic equation on the ball in $\mathbb {R}^3$},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     pages = {83--102},
     publisher = {Scuola normale superiore},
     volume = {Ser. 4, 18},
     number = {1},
     year = {1991},
     mrnumber = {1118222},
     zbl = {0774.35041},
     language = {en},
     url = {http://archive.numdam.org/item/ASNSP_1991_4_18_1_83_0/}
}
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
SP  - 83
EP  - 102
VL  - 18
IS  - 1
PB  - Scuola normale superiore
UR  - http://archive.numdam.org/item/ASNSP_1991_4_18_1_83_0/
LA  - en
ID  - ASNSP_1991_4_18_1_83_0
ER  - 
%0 Journal Article
%A Poláčik, Peter
%T Realization of any finite jet in a scalar semilinear parabolic equation on the ball in $\mathbb {R}^3$
%J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
%D 1991
%P 83-102
%V 18
%N 1
%I Scuola normale superiore
%U http://archive.numdam.org/item/ASNSP_1991_4_18_1_83_0/
%G en
%F ASNSP_1991_4_18_1_83_0
Poláčik, 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, Série 4, Tome 18 (1991) no. 1, pp. 83-102. http://archive.numdam.org/item/ASNSP_1991_4_18_1_83_0/

[Am] H. Amann, On abstract parabolic fundamental solutions, J. Math. Soc. Japan, 39 (1987), 93-116. | MR | Zbl

[Be] M.S. Berger, Nonlinearity and Functional Analysis, Academic Press, New York 1977. | MR | Zbl

[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, Novosibirsk 1988, 1-23.

[Ch-H] S.N. Chow - J.K. Hale, Methods of Bifurcation Theory, Springer-Verlag, New York 1982. | MR | Zbl

[Co-H] R. Courant - D. Hilbert, Methods of Mathematical Physics, Interscience, New York 1953. | MR | Zbl

[Da 1] E.N. Dancer, The effect of domain shape on the positive solutions of certain nonlinear equations, J. Differential Equations 74 (1988), 120-156. | MR | Zbl

[Da 2] E.N. Dancer, On the existence of two-dimensional invariant tori for scalar parabolic equations with time periodic coefficients, preprint.

[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. | MR | Zbl

[G-S] M. Golubitski - D. Schaeffer, Singularities and Groups in Bifurcation Theory, Appl. Math. Sci. 51, Springer-Verlag, New York 1986. | Zbl

[Ha 1] J.K. Hale, Flows on centre manifolds for scalar functional differential equations, Proc. Roy. Soc. Edinburgh, 101A (1985), 193-201. | MR | Zbl

[Ha 2] J.K. Hale, Local flows for functional differential equations, Contemp. Math. 56, Amer. Math. Soc., Providence 1986, 185-192. | MR | Zbl

[He] D. Henry, Geometric Theory of Semilinear Parabolic Equations, Lecture Notes in Math., 840, Springer-Verlag, New York 1981. | MR | Zbl

[Ka] T. Kato, Perturbation Theory for Linear Operators, Springer-Verlag, Berlin 1966. | MR | Zbl

[Ma] H. Matano, Convergence of solutions of one-dimensional semilinear parabolic equations, J. Math. Kyoto Univ. 18 (1978), 221-227. | MR | Zbl

[Po 1] P Poláčik, Convergence in smooth strongly monotone flows defined by semilinear parabolic equations, J. Differential Equations 79 (1989), 89-110. | MR | Zbl

[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. | MR | Zbl

[Po 3] P Poláčik, Complicated dynamics in scalar semilinear parabolic equations in higher space dimension, J. Differential Equations, 89 (1991), 244-271. | MR | Zbl

[Po 4] P Poláčik, Imbedding of any vector field in a scalar semilinear parabolic equation, Proc. AMS, to appear. | MR | Zbl

[Sm] V.I. Smirnov, A Course of Advanced Mathematics III2, Nauka, Moscow, 1974. | MR

[Ta] P Takáč, Domains of attraction of generic w-limit sets for strongly monotone semiflows, Z. Anal. Anwendungen, to appear. | MR | Zbl

[Tr] H. Triebel, Interpolation Theory, Function Spaces, Differential Operators, North Holland, Amsterdam 1978. | MR | Zbl

[Va] A. Vanderbauwhede, Local Bifurcation and Symmetry, Research Notes in Mathematics, Pitman, Boston 1982. | MR | Zbl

[Ze] T.J. Zelenyak, Stabilization of solutions of boundary value problems for a second order parabolic equations with one space variable, Differential Equations 4 (1968), pp. 17-22. | MR | Zbl