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New results on strongly coupled systems of parabolic differential equations

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Ordinary and Partial Differential Equations

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 564))

Abstract

The boundary value problem for a nonlinear, strongly coupled, parabolic system of differential equations is considered. Error bounds for an approximation are given, a uniqueness theorem is proved. The results are derived with the aid of the theory of differential inequalities and by using an inequality of Bernstein. The results are applied to the 3-dimensional Prandtl boundary layer equations.

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References

  1. Achieser, N.I.: Vorlesungen über Approximationstheorie. Akademie-Verlag, Berlin, 1953.

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  2. Bernstein, S.N.: Sur une propriété des fonctions entières. Comptes rendus, 176 (1923).

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  3. Lakshmikantham, V. and S. Leela: Differential and Integral Inequalities. Vol. I and II. Academic Press, New York and London, 1969.

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  4. Nickel, K.: Ein Eindeutigkeitssatz für instationäre Grenzschichten. Math. Z. 74 (1960), 209–220.

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  5. Nickel, K.: The Crocco-transformation for the three-dimensional Prandtl boundary layer equations. MRC Technical Summary Report No. 1594. Madison / Wisc. 1975.

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  6. Nickel, K.: Errorbounds and Uniqueness for the Solutions of nonlinear, strongly coupled, parabolic systems of differential equations. MRC Technical Summary Report No. 1596. Madison / Wisc. 1975.

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  7. Nickel, K.: On strongly coupled systems of nonlinear parabolic differential equations. To appear in russian in the proceedings of the conference in honor of the 75th birthday of I.G. Petrovski in Moscow, January 27 to 31, 1976.

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  8. Szarski, J.: Differential Inequalities. Monografie Matematiczne, Tom 43. Warszawa 1965.

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  9. Walter, W.: Differential and Integral Inequalities. Springer-Verlag 1970.

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Authors
  1. Karl Nickel
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Editor information

William N. Everitt Brian D. Sleeman

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© 1976 Springer-Verlag

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Nickel, K. (1976). New results on strongly coupled systems of parabolic differential equations. In: Everitt, W.N., Sleeman, B.D. (eds) Ordinary and Partial Differential Equations. Lecture Notes in Mathematics, vol 564. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0087352

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  • DOI: https://doi.org/10.1007/BFb0087352

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-08058-9

  • Online ISBN: 978-3-540-37517-3

  • eBook Packages: Springer Book Archive

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