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Semilinear waves with cusp singularities. (English) Zbl 0656.35098
Journ. Équ. Dériv. Partielles, St.-Jean-De-Monts 1987, Exp. No. 10, 10 p. (1987).
Let P be a second order strictly hyperbolic operator with \(C^{\infty}\) coefficients in some open domain \(\Omega \subset {\mathbb{R}}^{1+n}\). The propagation of conormal regularity for bounded solutions of the (weakly) semilinear hyperbolic equation \[ (*)\quad Pu(z)=g(z,u),\quad z\in \Omega,\quad u\in L^{\infty}_{loc}(\Omega),\quad g\in C^{\infty}(\Omega \times {\mathbb{R}}) \] will be described when the wavefront, a characteristic surface for P, has cusp singularities.

MSC:
35L70 Second-order nonlinear hyperbolic equations
35L67 Shocks and singularities for hyperbolic equations
35A27 Microlocal methods and methods of sheaf theory and homological algebra applied to PDEs
35B65 Smoothness and regularity of solutions to PDEs
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