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References
Beals, M., Nonlinear wave equations with data singular at one point (preprint).
Beals, M. andReed, M., Propagation of singularities for hyperbolic pseudo differential operators with non-smooth coefficients,Comm. Pure Appl. Math. 35 (1982), 169–184.
Bony, J.-M., Calcul symbolique et propagation des singularités pour les équations aux dérivées partielles nonlinéares,Ann. Sci. École Norm. Sup. 14 (1981), 209–246.
Bony, J.-M., Interaction des singularités pour les équations aux dérivées partielles non linéares,Sem. Goulaouic-Schwartz, 1979–1980, #22 andSem. Goulaouic-Meyer-Schwartz 1981–1982, #2.
Bony, J.-M., Second microlocalization and propagation of singularities for semi-linear hyperbolic equations. (preprint).
Melrose, R. B., Transformation of boundary problems,Acta Math. 147 (1981), 149–236.
Melrose, R. B. andRitter, N., Interaction of nonlinear progressing waves for semilinear wave equations,Ann. of Math. 121 (1985), 187–213.
Melrose, R. B. andUhlmann, G., Lagrangian intersection and the Cauchy problem,Comm. Pure Appl. Math. (1979), 483–519.
Rauch, J. andReed, M., Propagation of singularities for semilinear hyperbolic equations in one space variable,Ann. of Math. 111 (1980), 531–552.
Rauch, J. andReed, M., Singularities produced by the nonlinear interaction of three progressing waves; examples,Comm. Partial Differential Equations 7 (1982), 1117–1133.
Rauch, J. andReed, M., Nonlinear microlocal analysis of semilinear hyperbolic systems in one space dimension,Duke Math. J. 49 (1982), 397–475.
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The first author received partial support from National Science Foundation grant mcs 8306271 and the second was a National Science Foundation Post-Doctoral Fellow during the preparation of this manuscript.
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Melrose, R.B., Ritter, N. Interaction of progressing waves for semilinear wave equations. II. Ark. Mat. 25, 91–114 (1987). https://doi.org/10.1007/BF02384437
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DOI: https://doi.org/10.1007/BF02384437