Gerard, P.; Rauch, J. Propagation de la régularité locale de solutions d’équations hyperboliques non linéaires. (Propagation of local smoothness for solutions of nonlinear hyperbolic equations). (French) Zbl 0617.35079 Ann. Inst. Fourier 37, No. 3, 65-84 (1987). For each positive number s, we study the propagation of local smoothness \(H^ s\) for solutions of nonlinear hyperbolic equations, under assumptions of minimal smoothness allowing to define the nonlinear terms in the equation. In particular, we prove a theorem of propagation in the case of essentially bounded (resp. Lipschitz continuous) solutions of first order semilinear (resp. quasilinear) systems. Cited in 9 Documents MSC: 35L60 First-order nonlinear hyperbolic equations 35B40 Asymptotic behavior of solutions to PDEs 35B65 Smoothness and regularity of solutions to PDEs Keywords:propagation; local smoothness; nonlinear hyperbolic equations; Lipschitz continuous; first order semilinear; quasilinear × Cite Format Result Cite Review PDF Full Text: DOI Numdam EuDML References: [1] [1] , , Propagation de l’analyticité des solutions d’équations non linéaires de type principal, Comm. in P.D.E., (1984), 523-537. · Zbl 0566.35017 [2] [2] , Calcul symbolique et propagation des singularités pour les équations non linéaires, Ann. Scient. E.N.S., 14 (1981), 209-246. · Zbl 0495.35024 [3] [3] , Propagation des singularités pour les équations aux dérivées partielles non linéaires, Séminaire Goulaouic-Schwartz, n° 22, 1979-1980, Ecole Polytechnique, Paris. · Zbl 0449.35006 [4] [4] , , Introduction à la théorie des équations aux dérivées partielles linéaires, Gauthier-Villars, 1981. · Zbl 0446.35001 [5] [5] , , Au-delà des opérateurs pseudo-différentiels, Astérisque, vol. 57 (1978). · Zbl 0483.35082 [6] [6] , A note on Sobolev spaces, in Harmonic Analysis in Euclidean spaces, Proc. Symp. in Pure Mathematics (A.M.S), vol. 35, Part 1 (1979), 183-185. · Zbl 0421.46027 [7] [7] , Compressible fluid flows and systems of conservation laws in several variables, Applied Mathematical Sciences 33, Springer, 1984). · Zbl 0537.76001 [8] [8] , Remarque sur un théorème de J.-M. Bony, Suppl. ai Rendiconti del Circ. Mat. di Palermo, Atti del Seminario di Analisi Armonica, Pisa, Serie 2, n° 1, 1981. · Zbl 0473.35021 [9] [9] , Singularities of solutions of semilinear wave equations, J. Math. Pures et Appliquées, 58 (1979), 299-308. · Zbl 0388.35045 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.