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Bounds and domains of existence for hyperbolic initial value problems

Schranken und Existenzbereiche für hyperbolische Anfangswertaufgaben

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Abstract

Nonlinear hyperbolic initial value problems in plane regions are considered. By a discretization method which makes use of certain structure properties of the solutions\(\bar u\), a finite dimensional technique is constructed which provides pointwise bounds for\(\bar u\). At the same time, realistic informations on the domain of existence of\(\bar u\) can be obtained. The method's high degree of accuracy is shown by numerical examples.

Zusammenfassung

Nichtlineare hyperbolische Anfangswertaufgaben in ebenen Gebieten werden betrachtet. Mit Hilfe einer Diskretisierungsmethode, die Struktureigenschaften der Lösungen berücksichtigt, wird ein endlichdimensionales Verfahren konstruiert, das Schranken liefert. Gleichzeitig kann man realistische Informationen über den Existenzbereich der Lösung gewinnen. Die numerische Effektivität der Methode wird anhand von Beispielen demonstriert.

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References

  1. Hofmann, W.: Monotonie und finite Elemente bei zweidimensionalen hyperbolischen Anfangswertaufgaben. Preprint Nr. 78/8 des Inst. f. Ang. Math. der Universität Hamburg, Hamburg, 1978.

  2. Sprekels, J.: Finite dimensional cone iteration techniques for superlinear Hammerstein equations. (Submitted to Numerical Functional Analysis and Optimization.)

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  4. Walter, W.: Differential and integral inequalities. Berlin-Heidelberg-New York: Springer 1970.

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Authors and Affiliations

  1. Institut für Angewandte Mathematik, Universität Hamburg, Bundesstraße 55, D-2000, Hamburg 13, Federal Republic of Germany

    J. Sprekels

  2. Fachbereich Mathematik, Universität Essen-GHS, Universitätsstraße 2, D-4300, Essen, Federal Republic of Germany

    H. Voss

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  1. J. Sprekels
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  2. H. Voss
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Sprekels, J., Voss, H. Bounds and domains of existence for hyperbolic initial value problems. Computing 23, 73–83 (1979). https://doi.org/10.1007/BF02252615

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  • DOI: https://doi.org/10.1007/BF02252615

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