Remote Access Bulletin of the American Mathematical Society

Bulletin of the American Mathematical Society

ISSN 1088-9485(online) ISSN 0273-0979(print)

Book Review

The AMS does not provide abstracts of book reviews. You may download the entire review from the links below.

Full text of review: PDF   This review is available free of charge.
Book Information:

Author: Elemér E. Rosinger
Title: Generalized solutions of nonlinear partial differential equations
Additional book information: Mathematical Studies, vol. 146, North-Holland, Elsevier Science Publishers, Amsterdam, 1987, xvii + 409 pp., US $ 92.00; Dfl 175.00. ISBN 0-444-70310-1.

References [Enhancements On Off] (What's this?)

  • 1. Hebe A. Biagioni, A nonlinear theory of generalized functions, 2nd ed., Lecture Notes in Mathematics, vol. 1421, Springer-Verlag, Berlin, 1990. MR 1049623
  • 2. Jean-François Colombeau, New generalized functions and multiplication of distributions, North-Holland Mathematics Studies, vol. 84, North-Holland Publishing Co., Amsterdam, 1984. Notas de Matemática [Mathematical Notes], 90. MR 738781
  • 3. Jean-François Colombeau, Elementary introduction to new generalized functions, North-Holland Mathematics Studies, vol. 113, North-Holland Publishing Co., Amsterdam, 1985. Notes on Pure Mathematics, 103. MR 808961
  • 4. J.-F. Colombeau and A. Y. LeRoux, Multiplications of distributions in elasticity and hydrodynamics, J. Math. Phys. 29 (1988), no. 2, 315–319. MR 927013,
  • 5. Y. C. Fung, A first course in continuum mechanics, Prentice-Hall, Englewood Cliffs, N. J., 1969.
  • 6. J. Jelínek, Characterization of the Colombeau product of distributions, Comment. Math. Univ. Carolin. 27 (1986), no. 2, 377–394. MR 857556
  • 7. Lars Hörmander, The analysis of linear partial differential operators. I, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 256, Springer-Verlag, Berlin, 1983. Distribution theory and Fourier analysis. MR 717035
    Lars Hörmander, The analysis of linear partial differential operators. II, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 257, Springer-Verlag, Berlin, 1983. Differential operators with constant coefficients. MR 705278
  • 8. Hans Lewy, An example of a smooth linear partial differential equation without solution, Ann. of Math. (2) 66 (1957), 155–158. MR 0088629,
  • 9. J.-L. Lions, Quelques méthodes de résolution des problèmes aux limites non linéaires, Dunod; Gauthier-Villars, Paris, 1969 (French). MR 0259693
  • 10. M. Oberguggenberger, Products of distributions, J. Reine Angew. Math. 365 (1986), 1–11. MR 826149,
  • 11. Michael Oberguggenberger, Multiplication of distributions in the Colombeau algebra 𝒢(Ω), Boll. Un. Mat. Ital. A (6) 5 (1986), no. 3, 423–429 (English, with Italian summary). MR 866552
  • 12. Elemer E. Rosinger, Distributions and nonlinear partial differential equations, Lecture Notes in Mathematics, vol. 684, Springer, Berlin, 1978. MR 514014
  • 13. Elemer E. Rosinger, Nonlinear partial differential equations, North-Holland Mathematics Studies, vol. 44, North-Holland Publishing Co., Amsterdam-New York, 1980. Sequential and weak solutions; Notas de Matemática [Mathematical Notes], 73. MR 590891
  • 14. Laurent Schwartz, Sur l’impossibilité de la multiplication des distributions, C. R. Acad. Sci. Paris 239 (1954), 847–848 (French). MR 0064324
  • 15. François Trèves, Basic linear partial differential equations, Academic Press [A subsidiary of Harcourt Brace Jovanovich, Publishers], New York-London, 1975. Pure and Applied Mathematics, Vol. 62. MR 0447753

Review Information:

Reviewer: J. F. Colombeau
Journal: Bull. Amer. Math. Soc. 20 (1989), 96-101