Interaction of radially smooth nonlinear waves

M. Beals, Spreading of singularities for a semilinear wave equation, Duke Math. J. 49 (1982), 275–286.
Article MathSciNet MATH Google Scholar
_____, Self-spreading and strength of singularities for solutions to semilinear wave equations, Ann. of Math. 118 (1983), 187–214.
Article MathSciNet MATH Google Scholar
_____, Nonlinear wave equations with data singular at one point, Contemp. Math. 27 (1984), 83–95.
Article MathSciNet MATH Google Scholar
M. Beals and M. Reed, Propagation of singularities for hyperbolic pseudodifferential operators with nonsmooth coefficients, Comm. Pure Appl. Math. 35 (1982), 169–184.
Article MathSciNet MATH Google Scholar
J.-M. Bony, Calcul symbolique et propagation des singularités pour les équations aux deriveés partielles nonlineaires, Ann. Scien. de l'Ecole Norm. Sup. 14 (1981), 209–246.
MathSciNet MATH Google Scholar
_____, Interaction des singularités pour les équations aux deriveés partielles nonlineaires, Sem. Goulaouic-Meyer-Schwartz, exp. no. 22 (1979–80).
Google Scholar
_____, Interaction des singularités pour les équations de Klein-Gordon non lineaires, Sem. Goulaouic-Meyer-Schwartz, exp. no. 10 (1983–84).
Google Scholar
L. Hörmander, Fourier integral operators I, Acta Math. 127 (1971), 79–183.
Article MathSciNet MATH Google Scholar
R. Melrose and N. Ritter, Interaction of nonlinear progressing waves for semilinear wave equations, Ann. of Math. 121 (1985), 187–213.
Article MathSciNet MATH Google Scholar
_____, Interaction of progressing waves for semilinear wave equations II, preprint.
Google Scholar
J. Rauch and M. Reed, Propagation of singularities for semilinear hyperbolic equations in one space variable, Ann. of Math. 111 (1980), 531–552.
Article MathSciNet MATH Google Scholar
_____, Nonlinear microlocal analysis of semilinear hyperbolic systems in one space dimension, Duke Math. J. 49 (1982), 379–475.
Article MathSciNet MATH Google Scholar
_____, Singularities produced by the nonlinear interaction of three progressing waves: examples, Comm. P.D.E. 7 (1982), 1117–1133.
Article MathSciNet MATH Google Scholar
_____, Striated solutions of semilinear, two speed wave equations, Indiana U. Math. J. 34 (1985), 337–353.
Article MathSciNet MATH Google Scholar
_____, Bounded, stratified, and striated solutions of hyperbolic systems, preprint.
Google Scholar
Ya. G. Sinai, Introduction to Ergodic Theory, Princeton University Press, Princeton, N.J., 1976.
MATH Google Scholar
M. Taylor, Pseudodifferential Operators, Princeton University Press, Princeton, N.J., 1981.
MATH Google Scholar

Download references

Author information

Authors and Affiliations

Department of Mathematics, Rutgers University, 08903, New Brunswick, N.J.
Michael Beals

Authors

Michael Beals
View author publications
You can also search for this author in PubMed Google Scholar

Editor information

Heinz O. Cordes Bernhard Gramsch Harold Widom

Rights and permissions

Reprints and permissions

Copyright information

About this chapter

Cite this chapter

Beals, M. (1987). Interaction of radially smooth nonlinear waves. In: Cordes, H.O., Gramsch, B., Widom, H. (eds) Pseudo-Differential Operators. Lecture Notes in Mathematics, vol 1256. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0077735

Download citation

DOI: https://doi.org/10.1007/BFb0077735
Published: 19 September 2006
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-17856-9
Online ISBN: 978-3-540-47886-7
eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Interaction of radially smooth nonlinear waves

Access this chapter

Preview

References