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Book Review
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Book Information
Author(s):
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:
- 1.
- H. A. Biagioni, Introduction to a nonlinear theory of generalized functions (200 pp. ), Preprint series, Notas de Matematica, 1987, IMECC, UNICAMP, 13100, Campinas SP, Brazil. MR 1049623
- 2.
- J. F. Colombeau, New generalized functions and multiplication of distributions, North-Holland, Amsterdam, 1984. MR 738781
- 3.
- J. F. Colombeau, Elementary introduction to new generalized functions, North-Holland, Amsterdam, 1985. MR 808961
- 4.
- J. F. Colombeau and A. Y. Le Roux, Multiplications of distributions in elasticity and hydrodynamics, J. Math. Phys. 29 (1988), 315-319. MR 927013
- 5.
- Y. C. Fung, A first course in continuum mechanics, Prentice-Hall, Englewood Cliffs, N. J., 1969.
- 6.
- J. Jelinek, Characterization of the Colombeau product of distributions, Comment. Math. Univ. Carolinae 27 (1986), 377-394. MR 857556
- 7.
- L. Hörmander, The analysis of linear partial differential operators. I, II, Springer-Verlag, Berlin and New York, 1983. MR 717035
- 8.
- H. Lewy, An example of a smooth linear partial differential equation without solution, Ann. of Math. (2) 66 (1957), 155-158. MR 88629
- 9.
- J. L. Lions, Quelques méthodes de résolution des problèmes aux limites non linéaires, Dunod, Paris, 1969. MR 259693
- 10.
- M. Oberguggenberger, Products of distributions, J. Reine Angew. Math. 365 (1986), 1-11. MR 826149
- 11.
- M. Oberguggenberger, Multiplications of distributions in the Colombeau algebra B(Ω), Boll. Un. Mat. Ital. 5A (1986), 423-429. MR 866552
- 12.
- E. E. Rosinger, Distributions and nonlinear partial differential equations, Springer-Verlag, Berlin and New York, 1978. MR 514014
- 13.
- E. E. Rosinger, Nonlinear partial differential equations: sequential and weak solutions, North-Holland, Amsterdam, 1980. MR 590891
- 14.
- L. Schwartz, SUR l'impossibilité de la multiplication des distributions, C. R. Acad. Sci. Paris 239 (1954), 847-848. MR 64324
- 15.
- F. Treves, Basic linear partial differential equations, Academic Press, New York, 1978. MR 447753
Additional Information:
Reviewer(s):
J. F.
Colombeau
Review Information:
Journal:
Bull. Amer. Math. Soc.
20
(1989),
96-101.
DOI:
10.1090/S0273-0979-1989-15712-1
PII:
S 0273-0979(1989)15712-1
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