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Ein stabiles Schichtenverfahren für allgemeine lineare Evolutionsgleichungen

A stable line method for general linear evolution equations

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Summary

By generalizing Rothe's method of lines to initial value problemsu=A u, u(0)=u 0 in Banach-spaces one obtains an approximation method that can be investigated within the theory of Lax and richtmyer [2]. It is well known that the generalized solutions of properly posed problems are semi-groups of class (C0). In this paper the relation between the infinitesimal generator of that semi-group and the operatorA of the initial-value problem is discussed. As a consequence of the representation theorem of Hille-Yosida-Phillips one obtains that the method in question is stable iff the initial value problem is properly posed.

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Literatur

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Authors and Affiliations

  1. Mathematisches Institut der Universität München, Theresienstraße 39, D-8000, München 2, Bundesrepublik Deutschland

    U. v. Welck

Authors
  1. U. v. Welck
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Die Arbeit ist die gekürzte Fassung eines Teils meiner Dissertation [7], die ich am Lehrstuhl von Prof. G. Hämmerlin anfertigte. Ihm danke ich herzlich für die Unterstützung bei der Anfertigung der Arbeit.

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v. Welck, U. Ein stabiles Schichtenverfahren für allgemeine lineare Evolutionsgleichungen. Numer. Math. 27, 171–178 (1977). https://doi.org/10.1007/BF01396637

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  • DOI: https://doi.org/10.1007/BF01396637

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