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Stability results for a class of non-linear parabolic equations. (English) Zbl 0377.35039

MSC:
35K55 Nonlinear parabolic equations
35B40 Asymptotic behavior of solutions to PDEs
35P05 General topics in linear spectral theory for PDEs
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[1] Nonlinear problems in the physical sciences and biology (Proceedings of the Battelle Summer Institute, 1972), ed. byI. Stakgold, D. D. Joseph andD. H. Sattinger, Lecture Notes in Mathematics, no. 322, Springer (1973). · Zbl 0254.00025
[2] Eigenvalue of nonlinear problems, CIME Summer School, Varenna, 1974, ed. byG. Prodi, Cremonese (1974).
[3] Ambrosetti, A.; Prodi, G., Analisi non lineare. Quaderno I (1973), Pisa: Scuola Normale Superiore, Pisa · Zbl 0352.47001
[4] Aubin, T., Problèmes isopérimétriques et espaces de Sobolev, Comptes Rendus de l’Acad. des Sciences de Paris, 280, 279-281 (1975) · Zbl 0295.53024
[5] J. F. G. Auchmuty,Liapunov methods and equations of parabolic type, in Nonlinear problems ..., no. 1 above, pp. 1-14.
[6] V. Barbu, Semigrupuri de contractii nelineare in spatii Banach, Editura Academiei Române, 1974 (English transl.:Nonlinear semigroups and differential equations in Banach spaces, Ed. Acad. Române-Noordhoff International Publ., 1976).
[7] Chafee, N.; Infante, E. F., A bifurcation problem for a nonlinear partial differential equation of parabolic type, Applicable Anal., 4, 17-37 (1974) · Zbl 0296.35046
[8] Chafee, N., Asymptotic behaviour for solutions of a one-dimensional parabolic equation with homogeneous Neumann boundary conditions, Journ. Diff. Eq., 18, 111-134 (1975) · Zbl 0304.35008
[9] Crandall, M. G.; Rabinowitz, P. H., Bifurcation, perturbation of simple eigenvalues and linearized stability, Arch. Rat. Mech. Anal., 52, 161-180 (1973) · Zbl 0275.47044
[10] Datko, R., Extending a theorem of A. M. Liapunov to Hilbert spaces, Journ. Math. Anal. Appl., 32, 610-616 (1970) · Zbl 0211.16802
[11] Domshlak, Iu. I., On the asymptotic stability of the solution of a nonlinear parabolic system, Prikl. Math. Mech., 27, 1, 238-240 (1963) · Zbl 0146.12902
[12] W. Hahn,Theorie und Anwendung der direkten Methode von Liapunov, Springer (1959). · Zbl 0083.07804
[13] Hale, J. K., Dynamical systems and stability, Journ. Math. Anal. Appl., 26, 39-59 (1969) · Zbl 0179.13303
[14] J. P. LaSalle,An invariance principle in the theory of stability, in International Symposium on Differential Equations and Dynamical Systems, ed. byJ. K. Hale andJ. P. LaSalle, Academic Press (1967), pp. 277-286.
[15] J. L. Lions,Quelques méthodes de résolution des problèmes aux limites non linéaires, Dunod (1969). · Zbl 0189.40603
[16] V. V. Nemytskii -V. V. Stepanov,Qualitative theory of differential equations, Princeton Univ. Press (1960). · Zbl 0089.29502
[17] L. E. Payne,Improperly posed problems in partial differential equations, Regional Conference in Applied Mathematics, no. 22, Society for Industrial and Applied Mathematics (1975). · Zbl 0302.35003
[18] Rakhmatullina, L. F., On the problem of stability of the solution of the nonlinear heat-conduction equation, Prikl. Math. Mech., 25, 3, 880-883 (1961) · Zbl 0103.06404
[19] Sattinger, D. H., Stability of bifurcating solutions by Leray-Schauder degree, Arch. Rat. Mech. Anal., 43, 154-166 (1971) · Zbl 0232.34027
[20] Sattinger, D. H., Monotone methods in nonlinear elliptic and parabolic boundary value problems, Indiana Univ. Mathem. Journ., 21, 979-1000 (1972) · Zbl 0223.35038
[21] Stakgold, I., Branching of solutions of nonlinear equations, SIAM Rev., 13, 289-331 (1971) · Zbl 0199.20503
[22] I. Stakgold -L. E. Payne,Nonlinear problems in nuclear reactor analysis, in Nonlinear Problems ..., no. 1 above, pp. 298-307. · Zbl 0259.35025
[23] G. Stampacchia,Equations elliptiques du second ordre à coefficients discontinus, Les Presses de l’Université de Montréal (1966). · Zbl 0151.15501
[24] Talenti, G., Best constant in Sobolev inequality, Annali di Mat. Pura e Appl., 110, IV, 353-572 (1976) · Zbl 0353.46018
[25] M. M. Vainberg,Variational methods for the study of nonlinear problems, Holden-Day (1964).
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