Project Euclid

References

• 1. M. Adamczewski, J. F. Colombeau, and A. Y. Le Roux, Convergence of numerical schemes involving powers of the Dirac delta function, J. Math. Anal. Appl. 195 (1) 1990, 172-185.
  Zentralblatt MATH: 0691.65067
  Mathematical Reviews (MathSciNet): MR1031183
  Digital Object Identifier: doi:10.1016/0022-247X(90)90439-M
  
• 2. A. Y. Barka, J. F. Colombeau, and B. Perrot, A numerical modeling of the fluid/fluid acoustic dioptra, J. Acoustique (in press), 1989.
• 3. H. A. Biagioni, Introduction to a nonlinear theory of generalized functions, Notas de Matematica, IMECC, UNICAMP, 13100, Campinas, SP Brazil, 1988. Second edition: A nonlinear theory of generalized functions, Lecture Notes in Math., vol. 1421, Springer-Verlag, Berlin, Heidelberg, New York, 1990.
  Zentralblatt MATH: 0694.46032
  Mathematical Reviews (MathSciNet): MR1049623
  
• 4. N. N. Bogoliubov and D. V. Shirkov, Introduction to the theory of quantized fields, Interscience (various editions).
  Zentralblatt MATH: 0088.21701
  
• 5. J. J. Cauret, J. F. Colombeau, and A. Y. Le Roux, Discontinuous generalized solutions of nonlinear nonconservative hyperbolic equations, J. Math. Anal. Appl. 139 (2) (1989), 552-573.
  Zentralblatt MATH: 0691.35057
  Mathematical Reviews (MathSciNet): MR996979
  Digital Object Identifier: doi:10.1016/0022-247X(89)90129-7
  
• 6. J. F. Colombeau, Differential calculus and holomorphy: Real and complex analysis in locally convex spaces, North-Holland, Amsterdam, 1982.
  Zentralblatt MATH: 0506.46001
  Mathematical Reviews (MathSciNet): MR671252
  
• 7. J. F. Colombeau, A multiplication of distributions, J. Math. Anal. Appl. 94 (1) (1983), 96-115.
  Zentralblatt MATH: 0519.46045
  Mathematical Reviews (MathSciNet): MR701451
  Digital Object Identifier: doi:10.1016/0022-247X(83)90007-0
  
• 8. J. F. Colombeau, New generalized functions and multiplication of distributions, NorthHolland, Amsterdam, 1984.
  Zentralblatt MATH: 0532.46019
  Mathematical Reviews (MathSciNet): MR738781
  
• 9. J. F. Colombeau, Elementary introduction to new generalized functions, North-Holland, Amsterdam, 1985.
  Zentralblatt MATH: 0584.46024
  Mathematical Reviews (MathSciNet): MR808961
  
• 10. J. F. Colombeau, The elastoplastic shock problem as an example of the resolution of ambiguities in the multiplication of distributions, J. Math. Phys. 30 (10) (1989), 2273-2279.
  Zentralblatt MATH: 0711.73050
  Mathematical Reviews (MathSciNet): MR1016295
  Digital Object Identifier: doi:10.1063/1.528554
  
• 11. J. F. Colombeau, A method to obtain correct jump conditions from systems in non-conservative form: new formulas and new numerical schemes, Num. Appl. Math. (in press).
• 12. J. F. Colombeau and M. Langlais, An existence-uniqueness result for a nonlinear parabolic equation with Cauchy data distribution, J. Math. Anal. Appl. 145 (1) (1990), 186-196.
  Zentralblatt MATH: 0701.35042
  
• 13. J. F. Colombeau and A. Y. Le Roux, Numerical techniques in elastodynamics, Lecture Notes in Math., vol. 1270, Springer-Verlag, Berlin and New York, 1986, pp. 104-114.
  Zentralblatt MATH: 0644.73039
  
• 14. J. F. Colombeau and A. Y. Le Roux, Multiplications of distributions in elasticity and elastoplasticity, J. Math. Physics. 29 (2) (1988), 315-319.
  Zentralblatt MATH: 0646.76007
  Mathematical Reviews (MathSciNet): MR927013
  Digital Object Identifier: doi:10.1063/1.528069
  
• 15. J. F. Colombeau and A. Y. Le Roux, Numerical methods for hyperbolic systems in nonconservative form using products of distributions, Advances for computer methods in PDE 6 IMACS, 1987, pp. 28-37. Far better results can be found in: P. DeLuca Modelisation numérique en elastoplasticité dynamique, thesè, Bordeaux, 1989.
• 16. J. F. Colombeau and A. Y. Le Roux, Generalized functions and products appearing in equations of engineering and physics, preprint.
• 17. J. F. Colombeau, A. Y. Le Roux, A. Noussair, and B. Perrot, Microscopic profile of shock waves and ambiguities in multiplications of distributions, SIAM J. Numer. Anal. 26 (4) (1989), 871-882.
  Zentralblatt MATH: 0674.76049
  Mathematical Reviews (MathSciNet): MR1005514
  Digital Object Identifier: doi:10.1137/0726048
  
• 18. J. F. Colombeau and B. Perrot, A numerical method for the solution of nonlinear systems of physics involving multiplications of distributions, preprint.
• 19. R. Di Perna, Measure valued solutions to conservation laws, Arch. Rational Mech. Anal. 88 (1985), pp. 223-270.
  Zentralblatt MATH: 0616.35055
  Mathematical Reviews (MathSciNet): MR775191
  Digital Object Identifier: doi:10.1007/BF00752112
  
• 20. Y. C. Fung, A first course in continuum mechanics, Prentice Hall, Engle-wood Cliffs, NJ, 1969.
• 21. A. Marzouk and B. Perrot, Regularity results for generalized polutions of algebraic equations and algebraic differential equations, preprint.
• 22. M. Oberguggenberger, Products of distributions, J. Reine Angew. Math. 365 (1986), 1-11.
  Zentralblatt MATH: 0573.46019
  Mathematical Reviews (MathSciNet): MR826149
  
• 23. M. Oberguggenberger, Generalized solutions to semilinear hyperbolic systems, Monatshe. Math. 103(1987), 133-144.
  Zentralblatt MATH: 0615.35054
  Mathematical Reviews (MathSciNet): MR881719
  Digital Object Identifier: doi:10.1007/BF01630683
  
• 24. M. Oberguggenberger, Hyperbolic systems with discontinuous coefficients: generalized solution and a transmission problem in acoustics, J. Math. Anal. Appl. 42 (2) (1989), 452-467.
  Zentralblatt MATH: 0705.35146
  Mathematical Reviews (MathSciNet): MR1014590
  Digital Object Identifier: doi:10.1016/0022-247X(89)90014-0
  
• 25. M. Oberguggenberger, Hyperbolic systems with discontinuous coefficients: examples, Generalized Functions, Convergence Structure and Applications (B. Stankovic, E. Pap, S. Pilipovic, V. S. Vladimirov, eds.), Plenum, New York and London, 1988, pp. 257-266.
  Zentralblatt MATH: 0726.35133
  Mathematical Reviews (MathSciNet): MR975737
  Digital Object Identifier: doi:10.1007/978-1-4613-1055-6_26
  
• 26. E. E. Rosinger, Generalized solutions to Nonlinear PDE, North-Holland, Amsterdam, 1987.
  Mathematical Reviews (MathSciNet): MR918145
  
• 27. L. A. Rubel, Solutions of algebraic differential equations, J. Differential Equations 49 (1983), 441-452.
  Zentralblatt MATH: 0475.12029
  Mathematical Reviews (MathSciNet): MR715696
  Digital Object Identifier: doi:10.1016/0022-0396(83)90006-2
  
• 28. L. A. Rubel, Some research problems about algebraic differential equations, Trans. Amer. Math. Soc. 280 (1983), 43-52.
  Zentralblatt MATH: 0532.34009
  Mathematical Reviews (MathSciNet): MR712248
  Digital Object Identifier: doi:10.1090/S0002-9947-1983-0712248-1
  
• 29. L. A. Rubel, Generalized solutions of algebraic differential equations, J. Differential Equations 62 (1986), 242-251.
  Zentralblatt MATH: 0578.12017
  Mathematical Reviews (MathSciNet): MR833420
  Digital Object Identifier: doi:10.1016/0022-0396(86)90100-2