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Counterexamples for uniqueness in strongly coupled parabolic systems. (English) Zbl 0417.35047
MSC:
35K55 Nonlinear parabolic equations
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
35B35 Stability in context of PDEs
35B45 A priori estimates in context of PDEs
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References:
[1] Nickel, K.: Fehlerschranken und Eindeutigkeitsaussagen für die Lösungen nichtlinearer, stark gekoppelter parabolischer Differentialgleichungen. Math. Z.152, 33-34 (1976) · Zbl 0332.35038 · doi:10.1007/BF01214220
[2] Nickel, K.: The lemma of Max Müller-Nagumo-Westphal for strongly coupled systems of parabolic functional differential equations. MRC Report 800. Madison: University of Wisconsin 1977
[3] Redheffer, R., Walter, W.: Stability of the null solution of parabolic functional inequalities. Preprint · Zbl 0454.35015
[4] Redheffer, R., Walter, W.: The Total Variation of Solutions of Parabolic Differential Equations and a Maximum Principle in Unbounded Domains. Math. Ann.209, 57-67 (1974) · Zbl 0274.35040 · doi:10.1007/BF01432886
[5] Szarski, J.: Differential inequalities. Monographie Matematyczne43. Warszawa: Polska Akademia Nauk 1965
[6] Walter, W.: Differential and integral inequalities. Ergebnisse der Mathematik und ihrer Grenzgebiete55, Berlin-Heidelberg-New York: Springer 1970 · Zbl 0252.35005
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