@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://www.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://www.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://www.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://www.numdam.org/item/ASNSP_1991_4_18_1_83_0/
[Am] On abstract parabolic fundamental solutions, J. Math. Soc. Japan, 39 (1987), 93-116. | MR | Zbl
,[Be] Nonlinearity and Functional Analysis, Academic Press, New York 1977. | MR | Zbl
,[Bi] 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] Methods of Bifurcation Theory, Springer-Verlag, New York 1982. | MR | Zbl
- ,[Co-H] Methods of Mathematical Physics, Interscience, New York 1953. | MR | Zbl
- ,[Da 1] The effect of domain shape on the positive solutions of certain nonlinear equations, J. Differential Equations 74 (1988), 120-156. | MR | Zbl
,[Da 2] On the existence of two-dimensional invariant tori for scalar parabolic equations with time periodic coefficients, preprint.
,[F-P] 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] Singularities and Groups in Bifurcation Theory, Appl. Math. Sci. 51, Springer-Verlag, New York 1986. | Zbl
- ,[Ha 1] Flows on centre manifolds for scalar functional differential equations, Proc. Roy. Soc. Edinburgh, 101A (1985), 193-201. | MR | Zbl
,[Ha 2] Local flows for functional differential equations, Contemp. Math. 56, Amer. Math. Soc., Providence 1986, 185-192. | MR | Zbl
,[He] Geometric Theory of Semilinear Parabolic Equations, Lecture Notes in Math., 840, Springer-Verlag, New York 1981. | MR | Zbl
,[Ka] Perturbation Theory for Linear Operators, Springer-Verlag, Berlin 1966. | MR | Zbl
,[Ma] Convergence of solutions of one-dimensional semilinear parabolic equations, J. Math. Kyoto Univ. 18 (1978), 221-227. | MR | Zbl
,[Po 1] Convergence in smooth strongly monotone flows defined by semilinear parabolic equations, J. Differential Equations 79 (1989), 89-110. | MR | Zbl
,[Po 2] 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] Complicated dynamics in scalar semilinear parabolic equations in higher space dimension, J. Differential Equations, 89 (1991), 244-271. | MR | Zbl
,[Po 4] Imbedding of any vector field in a scalar semilinear parabolic equation, Proc. AMS, to appear. | MR | Zbl
,[Sm] A Course of Advanced Mathematics III2, Nauka, Moscow, 1974. | MR
,[Ta] Domains of attraction of generic w-limit sets for strongly monotone semiflows, Z. Anal. Anwendungen, to appear. | MR | Zbl
,[Tr] Interpolation Theory, Function Spaces, Differential Operators, North Holland, Amsterdam 1978. | MR | Zbl
,[Va] Local Bifurcation and Symmetry, Research Notes in Mathematics, Pitman, Boston 1982. | MR | Zbl
,[Ze] 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
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