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Redheffer, Ray; Walter, Wolfgang

Stability of the null solution of parabolic functional inequalities. (English) Zbl 0454.35015

Trans. Am. Math. Soc. 262, 285-302 (1980).
Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page
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Cited in 3 Documents

MSC:

35B35 Stability in context of PDEs
35K99 Parabolic equations and parabolic systems
35B99 Qualitative properties of solutions to partial differential equations

Keywords:

stability; parabolic functional inequalities; uniqueness; deviating arguments
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References:

[1] A. Kolmogoroff, On inequalities between upper bounds of consecutive derivatives of an arbitrary function defined on an infinite interval, Uchenye Zapiski Moskov. Gos. Univ. Matematika 30 (1939), 3 – 16 (Russian, with English summary). · JFM 65.1181.01
[2] Karl Nickel, The Crocco-transformation for the three-dimensional Prandtl boundary layer equations, MRC Report 1594, University of Wisconsin, 1975.
[3] -, Error bounds and uniqueness for the solutions of nonlinear strongly coupled parabolic systems of differential equations, MRC Report 1596, University of Wisconsin, 1975.
[4] -, Fehlerschranken und Eindeutigkeitsaussagan für die Lösungen nichtlinearer, stark gekoppelter parabolischer Differentialgleichungen. Math. Z. 152 (1976), 33-45. · Zbl 0332.35038
[5] Karl Nickel, New results on strongly coupled systems of parabolic differential equations, Ordinary and partial differential equations (Proc. Fourth Conf., Univ. Dundee, Dundee, 1976) Springer, Berlin, 1976, pp. 350 – 364. Lecture Notes in Math., Vol. 564. · Zbl 0346.35064
[6] -, The lemma of Max Müller-Nagumo-Westphal for strongly coupled systems of parabolic functional differential equations, MRC Report 1800, 1977. (German transl, available from the University of Freiburg.)
[7] Raymond M. Redheffer, Die Collatzsche Monotonie bei Anfangswertproblemen, Arch. Rational Mech. Anal. 14 (1963), 196 – 212 (German). · Zbl 0116.30001 · doi:10.1007/BF00250702
[8] Ray Redheffer and Wolfgang Walter, Existence theorems for strongly coupled systems of partial differential equations over Bernstein classes, Bull. Amer. Math. Soc. 82 (1976), no. 6, 899 – 902. · Zbl 0349.35015
[9] R. M. Redheffer, Uniqueness, stability and error estimation for parabolic functional-differential equations, Ber. 9, Univ. Karlsruhe (1976). Accepted by the Soviet Academy of Sciences in October, 1976 for the Jubilee Volume dedicated to the 70th anniversary of Academician I. N. Vekua.
[10] Ray Redheffer and Wolfgang Walter, Das Maximumprinzip in unbeschränkten Gebieten für parabolische Ungleichungen mit Funktionalen, Math. Ann. 226 (1977), no. 2, 155 – 170 (German). · Zbl 0328.35005 · doi:10.1007/BF01360866
[11] Ray Redheffer and Wolfgang Walter, Inequalities involving derivatives, Pacific J. Math. 85 (1979), no. 1, 165 – 178. · Zbl 0431.26006
[12] Raymond Redheffer and Wolfgang Walter, Comparison theorems for parabolic functional inequalities, Pacific J. Math. 85 (1979), no. 2, 447 – 470. · Zbl 0449.35106
[13] -, Nonuniqueness of the null solution for strongly coupled systems of parabolic differential equations, Math. Z. 171 (1980), 83-90.
[14] Jacek Szarski, Differential inequalities, Monografie Matematyczne, Tom 43, Państwowe Wydawnictwo Naukowe, Warsaw, 1965. · Zbl 0503.35044
[15] Wolfgang Walter, Differential and integral inequalities, Translated from the German by Lisa Rosenblatt and Lawrence Shampine. Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 55, Springer-Verlag, New York-Berlin, 1970. · Zbl 0252.35005
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