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A stability analysis for a semi-linear parabolic partial differential equation.(English)Zbl 0271.35043


MSC:

35K55 Nonlinear parabolic equations
35B35 Stability in context of PDEs

Cite

References:

[1]Arima, R.; Hasegawa, Y., On global solutions for mixed problem of a semilinear differential equation, (Proc. Japan Acad, 39 (1963)), 721-725, (10) ·Zbl 0173.11804
[2]Auchmuty, J. F.G, Lyapunov methods and equations of parabolic type, (Proceedings Batelle Summer Institute on Applications of Non-Linear Analysis. Proceedings Batelle Summer Institute on Applications of Non-Linear Analysis, Springer-Verlag Lecture Notes (1972)), to be published in ·Zbl 0269.35057
[3]N. Chafee and E. F. InfanteApplicable Anal.;N. Chafee and E. F. InfanteApplicable Anal. ·Zbl 0296.35046
[4]Friedman, A., Partial Differential Equations of Parabolic Type (1964), Prentice-Hall: Prentice-Hall New Jersey ·Zbl 0144.34903
[5]Hale, J. K.; Infante, E. F., Extended dynamical systems and stability theory, (Proc. Nat. Acad. Sci. USA, 58 (1967)), 405-409, no. 2 ·Zbl 0155.42301
[6]Hale, J. K., Dynamical systems and stability, J. Math. Anal. Appl, 26, 35-59 (1969) ·Zbl 0179.13303
[7]Kanel, Ya. I., On the stability of solutions for a Cauchy problem involving an equation encountered in the theory of combustion, Mat. Sbornik, 59, 245-288 (1962) ·Zbl 0152.10302
[8]Kolmogoroff, A.; Petrovsky, I.; Piscounoff, N., Étude de l’équation de la diffusion avec croissance de la quantité de matière et son application à un problème biologique, Bulletin de l’Université d’État à Moscou, Série Internationale, vol. I (1937) ·Zbl 0018.32106
[9]LaSalle, J. P., An invariance principle in the theory of stability, (Hale, J. K.; LaSalle, J. P., Int. Symp. Diff. Eqs. Dyn. Sys (1967), Academic Press: Academic Press New York), 277-286 ·Zbl 0183.09401
[10]Protter, M. H.; Weinberger, H. F., Maximum Principles in Differential Equations (1967), Prentice-Hall: Prentice-Hall Englewood Cliffs, New Jersey ·Zbl 0153.13602
[11]Nagumo, J.; Arimoto, S.; Yoshizawa, S., An active pulse transmission line simulating nerve axon, (Proc. IRE, 50 (1962)), 2061-2070
[12]Nagumo, J.; Yoshizawa, S.; Arimoto, S., Bistable transmission lines, IEEE Transactions on Circuit Theory, CT-12, no. 3, 400-412 (1965)
[13]Sattinger, D. H., Monotone methods in nonlinear elliptic and parabolic boundary value problems, Indiana Univ. Math. J, 21, 979-1000 (1972) ·Zbl 0223.35038
[14]Sattinger, D. H., Topics in Stability and Bifurcation Theory (1973), Springer-Verlag: Springer-Verlag New York ·Zbl 0268.35042
[15]Sobolev, S. L., Partial Differential Equations of Mathematical Physics (1964), Pergamon: Pergamon New York ·Zbl 0123.06508
[16]Taylor, A., Introduction to Functional Analysis (1958), John Wiley & Sons, Inc: John Wiley & Sons, Inc New York ·Zbl 0081.10202
[17]Yamaguti, M., The asymptotic behaviour of the solution of a semi-linear partial differential equation related to an active pulse transmission line, (Proc. Japan Acad, 39 (1963)), 726-730, (10) ·Zbl 0173.11901
[18]Yoshizawa, S., Population growth process described by a semilinear parabolic equation, Math. Biosci, 7, 291-303 (1970) ·Zbl 0212.52102
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
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