Free Access
Issue
Math. Model. Nat. Phenom.
Volume 11, Number 2, 2016
Spectral problems
Page(s) 89 - 99
DOI https://doi.org/10.1051/mmnp/201611207
Published online 21 March 2016
  1. E. Allaud, V. Dévoué. Generalized solutions to a characteristic Cauchy problem. J. Appl. Anal., 19 (2013), 1–29. [CrossRef] [MathSciNet] [Google Scholar]
  2. J.-F. Colombeau. New Generalized Functions and Multiplication of Distributions. North-Holland, Amsterdam, Oxford, New-York, 1984. [Google Scholar]
  3. A. Delcroix. Topology and functoriality in (C,E,P) -algebras. Application to singular differential problems. J. Math. Anal. Appl., 359 (2008), 394–403. Doi: 10.1016/j.jmaa.2009.05.046 [CrossRef] [Google Scholar]
  4. A. Delcroix. A new approach to temperate generalized Colombeau functions. Publ. Inst. Math. Beograd, N.S., 84 (2008), no. 98, 109–121. Doi: 10.2298/PIM0898109D [Google Scholar]
  5. A. Delcroix, V. Dévoué, J.-A. Marti. Generalized solutions of singular differential problems. Relationship with classical solutions. J. Math. Anal. Appl., 353 (2009), 386–402. Doi: 10.1016/j.jmaa.2008.11.077J. [CrossRef] [Google Scholar]
  6. A. Delcroix, D. Scarpalézos. Topology on Asymptotic Algebras of Generalized Functions and Applications. Monatsh. Math., 129 (2000), 1–14. [CrossRef] [MathSciNet] [Google Scholar]
  7. V. Dévoué. On generalized solutions to the wave equation in canonical form. Dissertationes math., 443 (2007), 1–69. [CrossRef] [Google Scholar]
  8. V. Dévoué. Generalized solutions to a non Lipschitz Cauchy problem. J. Appl. Anal., 15 (2009), no. 1, 1–32. [CrossRef] [MathSciNet] [Google Scholar]
  9. Yu V Egorov. On the solubility of differential equations with simple characteristics. Russ. Math. Surv., 26 (1971), 113-130. [CrossRef] [Google Scholar]
  10. L. Gårding, T. Kotake, J. Leray. Uniformisation et développement asymptotique de la solution du problème de Cauchy linéaire à données holomorphes; analogue avec la théorie des ondes asymptotiques et approchées. Bull. Soc. Math. France, 92 (1964), 263–361. [MathSciNet] [Google Scholar]
  11. M. Grosser, M. Kunzinger, M. Oberguggenberger, R. Steinbauer. Geometric Theory of Generalized Functions with Applications to General Relativity. Kluwer Academic Publ., Dordrecht, 2001. [Google Scholar]
  12. M. Hasler, J.-A. Marti. Functorial methods in asymptotic extensions of topological algebras. Preprint (2009). [Google Scholar]
  13. L. Hörmander. On the characteristic Cauchy problem. Ann. Math., 88 (1968), 341-370. [CrossRef] [Google Scholar]
  14. J.-A. Marti. (C,E,P) -Sheaf structure and applications. In: Nonlinear theory of generalized functions. M. Grosser and alii, Eds. Research notes in mathematics. Chapman & Hall/CRC, (1999), 175–186 [Google Scholar]
  15. J.-A. Marti. Non linear Algebraic analysis of delta shock wave to Burgers’ equation. Pacific J. Math., 210 (2003), no. 1, 165–187. [CrossRef] [MathSciNet] [Google Scholar]
  16. M. Nedeljkov, S. Pilipović, D. Scarpalezos. The linear theory of Colombeau generalized functions. Pitman Research Notes in Mathematics Series 385, Longman Scientific & Technical, Harlow, 1998. [Google Scholar]
  17. M. Oberguggenberger. Multiplication of Distributions and Applications to Partial Differential Equations.Pitman Research Notes in Mathematics 259, Longman Scientific & Technical, Harlow, 1992. [Google Scholar]
  18. M. Oberguggenberger. Generalized solutions to nonlinear wave equations. Matemàtica Contemporânea, 27 (2004), 169–187. [MathSciNet] [Google Scholar]
  19. S. Pilipovic, D. Scarpalézos. Divergent type quasilinear Dirichlet problem. Acta Appl. Math., 94 (2006), 67–82 [CrossRef] [Google Scholar]
  20. H. Vernaeve. Pointwise Characterizations in generalized function algebras. Monatsh. Math., 158 (2009), 195–213. [CrossRef] [MathSciNet] [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.