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On the stability of bifurcation branches in thermal ignition

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Summary

A method is given to determine the stability of stationary solutions of the thermal ignition equation for the case ofn-dimensional spherical symmetry, together with the number of unstable modes. For sufficiently high temperature and activation temperature this number is arbitrarily large. Some numerical results on the solutions and their stability are reported.

Zusammenfassung

Ein Verfahren zur Bestimmung der Stabilität stationärer Lösungen der Gleichung der thermischen Selbstzündung imn-dimensionalen kugelsymmetrischen Fall sowie der Anzahl instabiler Eigenfunktionen wird angegeben. Für genügend hohe Temperatur und Aktivierungstemperatur ist diese Anzahl beliebig groß. Einige numerische Ergebnisse über die Lösungen und ihre Stabilität werden berichtet.

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Authors and Affiliations

  1. Fachbereich Mathematik der Johannes Gutenberg-Universität, D-6500, Mainz, W. Germany

    W. Börsch-Supan

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  1. W. Börsch-Supan
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Additional information

Part of this work has been done during the author's stay at the Applied Physics Laboratory of Johns Hopkins University Laurel Maryland USA

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Börsch-Supan, W. On the stability of bifurcation branches in thermal ignition. Z. angew. Math. Phys. 35, 332–344 (1984). https://doi.org/10.1007/BF00944882

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  • DOI: https://doi.org/10.1007/BF00944882

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