The Morse-Smale property for a semilinear parabolic equation. (English) Zbl 0581.58026

See the preview in Zbl 0548.58019.


37D15 Morse-Smale systems


Zbl 0548.58019
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[1] Agmon, S., Unicité et convexité dans les problèmes différentiels, Lect. Notes Univ. of Montreal (1966) · Zbl 0147.07702
[2] Chaffee, N., Asymptotic behaviour for solutions of a one-dimensional parabolic equation with homogeneous Neumann boundary conditions, J. Differential Equations, 18, 111-134 (1975) · Zbl 0304.35008
[3] Dieudonné, Foundations of Modern Analysis, ((1969), Academic Press: Academic Press New York), 357, Ex. XI.7.3 · Zbl 0967.01024
[4] Hale, J. K., Dynamics in a parabolic equation an example, (Ball, J. M., Systems of Nonlinear Partial Differential Equations (1983), Reidel: Reidel Dordrecht), 461-472 · Zbl 0524.35053
[5] Hale, J. K.; Magelhães, L. T.; Oliva, W. M., An Introduction to Infinite Dimensional Dynamical Systems—Geometric Theory, (Appl. Math. Sci., Vol. 47 (1984), Springer-Verlag: Springer-Verlag New York) · Zbl 0533.58001
[6] Henry, D., Geometric Theory of Semilinear Parabolic Equations, (Lecture Notes in Math., Vol. 840 (1981), Springer-Verlag: Springer-Verlag New York) · Zbl 0456.35001
[7] Lees, M.; Protter, M. H., Unique continuation for parabolic differential equations and inequalities, Duke Math. J., 28, 369-382 (1961) · Zbl 0143.33301
[8] Lions, J. L.; Malgrange, B., Sur l’unicité rétrograde dans les problèmes mixtes paraboliques, Math. Scand., 8, 277-286 (1960) · Zbl 0126.12202
[9] Matano, H., Non increase of the lapnumber of a solution for a one dimensional semilinear parabolic equation, J. Fac. Sci. Univ. Tokyo IA Math., 29, No. 2, 401-441 (1982) · Zbl 0496.35011
[10] Pazy, A., Semigroups of Linear Operators and Applications to Partial Differential Equations, (Appl. Math. Sci., Vol. 44 (1983), Springer-Verlag: Springer-Verlag New York) · Zbl 0516.47023
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