Hostname: page-component-78c5997874-8bhkd Total loading time: 0 Render date: 2024-11-11T09:34:28.453Z Has data issue: false hasContentIssue false
  • English
  • Français

Propagation Of Singularities for Semilinear Hyperbolic Equations

Published online by Cambridge University Press:  20 November 2018

Linqi Liu
Linqi Liu*
Affiliation:
Department of Mathematics and Statistics, York University, 4700 Keele Street, North York, Ontario, M3J 1P3
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this paper we use a particular kind of weighted Sobolev space and pseudo-differential operators to study H3s propagation of singularities for the solution u ∊ Hs of the equations with second order.

Keywords

35L7035A40
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 45 , Issue 4 , 01 August 1993 , pp. 835 - 846
Copyright
Copyright © Canadian Mathematical Society 1993

References

1. Beals, M., Singularities in solutions to nonlinear hyperbolic problems, preprint.Google Scholar
2. Beals, M., Propagation of smoothness for nonlinear second order strictly hyperbolic differential equations, A.M.S. Proc. Symp. Pure Math. 43(1985).Google Scholar
3. Beals, M., Self-spreading and strength of singularities for solutions to semilinear wave equations, Ann. of Math. 118(1983), 187–214.Google Scholar
4. Beals, M. and Reed, M., Propagation of singularities for hyperbolic pseudo-differential operators with non-smooth coefficients, Comm. Pure Appl. Math. XXXV(1982), 169–184.Google Scholar
5. Bony, J. M., Calcul symbolique et propagation des singularities pour les équation aux dérivées partielles non linéares, Ann. Sci. Ec. Norm. Sup. (4) ème série 14(1981), 209–246.Google Scholar
6. Chemin, J. Y., Interaction contrôlée dans les équations aux dérivées partielles nonlinéaires, C. R. Acad. Sci. Paris Sér. I Math. (10) 303(1986), 451–453.Google Scholar
7. Lascar, B., Singularités des solutions d'équations aux dérivées partielles nonlinéaires, C. R. Acad. Sci. Paris 287(1978), 521–529.Google Scholar
8. Nirenberg, L., Lectures on linear partial differential equations, CBMS Reg. Conf. Ser. in Math. 17, Amer. Math. Soc, Providence, R.I. (1973).Google Scholar
9. Liu, Linqi, Propagation of singularities for solutions of semilinear wave equations, Chin. Ann. of Math. (4)9B(1988).Google Scholar
10. Liu, Linqi, Propagation of stronger singularities of solutions to semilinear wave equations, Microlocal Analysis and Nonlinear Waves, (eds. M. Beals, R. Melrose and J. Rauch), the IMA volume 30 in Mathematics and It's Applications, Springer-Verlag, 1991.Google Scholar
11. Rauch, J., Singularities of solutions of semilinear wave equations, J. Math. Pures et Appl. 58(1979), 299–308.Google Scholar
12. Rauch, J. and Reed, M., Nonlinear microlocal analysis of semilinear hyperbolic systems in one space dimension, Duke Math. J. 49(1982), 397–475.Google Scholar