zbMATH — the first resource for mathematics

Globally smooth solutions of quasilinear hyperbolic systems in diagonal form. (English) Zbl 0488.35057

35L60 First-order nonlinear hyperbolic equations
35R05 PDEs with low regular coefficients and/or low regular data
35B65 Smoothness and regularity of solutions to PDEs
35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs
Full Text: DOI
[1] Diperna, R.J, Uniqueness of solutions to hyperbolic conservation laws, Indiana univ. math. J., 28, No. 1, (1979) · Zbl 0434.35061
[2] Friedrichs, K.O, Nonlinear hyperbolic differential equations for functions of two independent variables, Amer. J. math., 70, (1948) · Zbl 0039.10601
[3] \scD. Hoff, A constructive theory for shock-free, isentropic flow, J. Differential Equations, in press. · Zbl 0416.76015
[4] \scD. Hoff, Locally Lipschitz solutions of a single conservation law in several space variables, to appear. · Zbl 0443.34005
[5] Hurewicz, W, Lectures on ordinary differential equations, (1958), MIT Press Cambridge, Mass · Zbl 0082.29702
[6] John, F, Formation of singularities in one-dimensional nonlinear wave propogation, Comm. pure appl. math., 27, (1974)
[7] Lax, P.D, Nonlinear hyperbolic equations, Comm. pure appl. math., 6, (1953) · Zbl 0057.32502
[8] Lax, P.D, Development of singularities of solutions of nonlinear hyperbolic partial differential equations, J. math. phys., 5, No. 5, (1964) · Zbl 0135.15101
[9] Liu, Tai-Ping, Development of singularities in the nonlinear waves for quasi-linear hyperbolic partial differential equations, J. differential equations, 33, No. 1, (1979) · Zbl 0379.35048
[10] Yamaguti, M; Nishida, T, On some global solutions of quasilinear hyperbolic systems, Funkcial. ekvac., 11, (1968) · Zbl 0183.38601
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.