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http://yadda.icm.edu.pl:80/baztech/element/bwmeta1.element.baztech-article-LOD6-0004-0008

Czasopismo

Journal of Applied Analysis

Tytuł artykułu

Modelling and products of singularities in Colombeau's algebra G (R)

Autorzy Damyanov, B. 
Treść / Zawartość
Warianty tytułu
Języki publikacji EN
Abstrakty
EN Modeling of singularities given by discontinuos functions or Schwartz distributions by means of generalized functions of Colombeau has proved useful in many problems posed by physical phenomena. We introduce in a systematic way generalized functions that model singularities given by distributions with singular point support. Moreover, we evaluate various products of singularity-modelling generalized functions whenever the result admits an associated distribution.
Słowa kluczowe
EN Colombeau's algebra   singular products of distributions  
Wydawca Walter de Gruyter GmbH & Co. KG
Czasopismo Journal of Applied Analysis
Rocznik 2008
Tom Vol. 14, nr 1
Strony 89--102
Opis fizyczny Bibliogr. 8 poz.
Twórcy
autor Damyanov, B.
  • Bulgarian Academy of Science. INRNE-Theor. Math. Physics Dept. 72 Tzarigradsko Shosse, 1784 Sofia, Bulgaria, bdamyanov@mail.bg
Bibliografia
[1] Colombeau, J.-F., New Generalized Functions and Multiplication of Distributions, North-Holland Math. Studies 84, North-Holland Publ. Co., Amsterdam, 1984.
[2] Colombeau, J.-F., Le Roux, A. Y., Numerical methods for hyperbolic systems in nonconservative form using products of distributions, in "Advances in Computer Methods for Partial Differential Equations VI" , R. Vichnevetsky, R. S. Steplemen (eds.), IMACS, 1987, 28-37.
[3] Colombeau, J.-F., Le Roux, A. Y., Nuissair, A., Perrot, B., Microscopic profiles of shock waves and ambiguities in multiplication of distributions, SIAM J. Numer. Anal 26 (1989),871-883.
[4] Grosser, M., Kunzinger, M., Oberguggenberger, M., Steinbauer, R., Geometric Theory of Generalized Functions with Applications to General Relativity, Kluwer Acad. Publ., Dordrecht, 2001.
[5] Hermann, R., Oberguggenberger, M., ODEs and generalized junctions, in "Nonlinear Theory of Generalized Functions", M. Grosser, G. Hormann, M. Kunzinger, M. Oberguggenberger (eds.), Chapman & Hall/CRC, Boca Raton, 1999.
[6] Korn, G. A., Korn, T. M., Mathematical Handbook, McGraw-Hill Book Company, New York, 1968.
[7] Oberguggenberger, M., Multiplication of Distributions and Applications to PDEs, Longman, Essex, 1992.
[8] Steinbauer, R., Geodesics and geodesic derivation for impulsive waves, J. Math. Phys. 38 (1997),1614-1622.
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