Bulletin of the American Mathematical Society

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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.

Hebe A. Biagioni, A nonlinear theory of generalized functions, 2nd ed., Lecture Notes in Mathematics, vol. 1421, Springer-Verlag, Berlin, 1990. MR 1049623, DOI 10.1007/BFb0089552

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

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

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, DOI 10.1063/1.528069

5.

Y. C. Fung, A first course in continuum mechanics, Prentice-Hall, Englewood Cliffs, N. J., 1969.

J. Jelínek, Characterization of the Colombeau product of distributions, Comment. Math. Univ. Carolin. 27 (1986), no. 2, 377–394. MR 857556

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, DOI 10.1007/978-3-642-96750-4

Hans Lewy, An example of a smooth linear partial differential equation without solution, Ann. of Math. (2) 66 (1957), 155–158. MR 88629, DOI 10.2307/1970121

J.-L. Lions, Quelques méthodes de résolution des problèmes aux limites non linéaires, Dunod, Paris; Gauthier-Villars, Paris, 1969 (French). MR 0259693

M. Oberguggenberger, Products of distributions, J. Reine Angew. Math. 365 (1986), 1–11. MR 826149, DOI 10.1515/crll.1986.365.1

Michael Oberguggenberger, Multiplication of distributions in the Colombeau algebra ${\scr G}(\Omega )$, Boll. Un. Mat. Ital. A (6) 5 (1986), no. 3, 423–429 (English, with Italian summary). MR 866552

Elemer E. Rosinger, Distributions and nonlinear partial differential equations, Lecture Notes in Mathematics, vol. 684, Springer, Berlin, 1978. MR 514014

Elemer E. Rosinger, Nonlinear partial differential equations, Notas de Matemática [Mathematical Notes], vol. 73, North-Holland Publishing Co., Amsterdam-New York, 1980. Sequential and weak solutions. MR 590891

Laurent Schwartz, Sur l’impossibilité de la multiplication des distributions, C. R. Acad. Sci. Paris 239 (1954), 847–848 (French). MR 64324

François Trèves, Basic linear partial differential equations, Pure and Applied Mathematics, Vol. 62, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1975. MR 0447753

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