Regularized derivatives in a 2-dimensional model of self-interacting fields with singular data

Zeitschrift für Analysis und ihre Anwendungen

Volumn 19, Issue 1, 2000, Pages 147-158

  Hormann G ^a   Kunzinger, M ^a  

^a UNIVERSITY OF VIENNA   (Austria)

Author keywords

Colombeau algebras; Maxwell Lorentz system; Regularized derivatives; Self interaction; Weak hyperbolicity

Indexed keywords

EID: 26144456910     PISSN: 02322064     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (17)

1. Clarke, C. J. S., Vickers, J. A. and J. P. Wilson: Generalized functions and distributional curvature of cosmic strings. Class. Quant. Grav. 13 (1996), 2485 - 2498.
2. Colombeau, J. F.: New Generalized Functions and Multiplication of Distributions. Amsterdam: North Holland 1984.
3. Colombeau, J. F.: Elementary Introduction to New Generalized Functions. Amsterdam: North Holland 1985.
4. Colombeau, J. F. and A. Heibig: Generalized solutions to Cauchy problems. Monatsh. Math. 117 (1994), 33 - 49.
5. Colombeau, J. F., Heibig, A. and M. Oberguggenberger: Le probleme de Cauchy dans un espace de fonctions generalisees. Part I. C.R. Acad. Sci. (Ser. I) 317 (1993), 851 - 855.
6. Colombeau, J. F., Heibig, A. and M. Oberguggenberger: Le probleme de Cauchy dans un espace de fonctions generalisees. Part II. C.R. Acad. Sci. (Ser. I) 319 (1994), 1179 - 1183.
7. Colombeau, J. F., Heibig, A. and M. Oberguggenberger: Generalized solutions to partial differential equations of evolution type. Acta Appl. Math. 45 (1996), 115 - 142.
8. Hermann, R. and M. Oberguggenberger: Generalized functions, calculus of variations, and nonlinear ODEs. Preprint 1997.
9. Hermann, R. and M. Oberguggenberger: Ordinary differential equations and generalized functions. In: Nonlinear Theory of Generalized Functions (CRC-Res. Notes Math. 401; eds.: M. Grosser et al.). Boca Raton: CRC-Press 1999 (to appear).
10. Hörmann, G. and M. Kunzinger: Nonlinearity and self-interaction in physical field theories with singularities. Int. Transf. Spec. Funct. 6 (1998), 205 - 214.
11. Oberguggenberger, M.: Multiplication of Distributions and Applications to Partial Differential Equations (Pitman Research Notes in Mathematics: Vol. 259). Harlow: Longman 1992.
12. Parrott, S.: Relativistic Electrodynamics and Differential Geometry. New York: Springer 1987.
13. Rauch, J.: Partial Differential Equations. New York: Springer 1991.
14. Steinbauer, R.: The ultrarelativistic Reissner-Nordstrøm field in the Colombeau algebra. J. Math. Phys. 38 (1997), 1614 - 1622.
15. Steinbauer, R.: Geodesics and geodesic deviation for impulsive gravitational waves. J. Math. Phys. 39 (1998), 2201 - 2212.
16. Thirring, W.: A Course in Mathematical Physics. Vol. II. New York: Springer 1979.
17. Wilson, J. P.: Distributional curvature of time-dependent cosmic strings. Class. Quant. Grav. 14 (1997), 3337 - 3351.