The Cauchy problem for quasi-linear symmetric hyperbolic systems

1. Kato, T., Linear evolution equations of “hyperbolic” type. J. Fac. Sci. Univ. Tokyo 17, 241–258 (1970).

   Google Scholar 

2. Kato, T., Linear evolution equations of “hyperbolic type”, II. J. Math. Soc. Japan 25, 648–666 (1973).

   Google Scholar 

3. Friedrichs, K.O., Symmetric hyperbolic linear differential equations. Comm. Pure Appl. Math. 7, 345–392 (1954).

   Google Scholar 

4. Sobolev, S.L., Applications of functional analysis in mathematical physics. AMS Translations of Math. Monographs. 7, 1963.

5. Fischer, A.E., & J.E. Marsden, The Einstein evolution equations as a first-order quasi-linear symmetric hyperbolic systems, I. Commun. Math. Phys. 28, 1–38 (1972).

   Google Scholar 

6. Bers, L., F. John, & M. Schechter, Partial Differential Equations. Interscience 1964.

7. Kallman, R.R., & G.-C. Rota, On the inequality ‖f′‖² ≦ 4 ‖f‖ ‖f″‖. Inequalities, Vol. 2, pp. 187–192. Academic Press 1970.

8. Hormander, L., Linear partial differential operators. Springer 1963.

9. Massey, F.J. III, Abstract evolution equations and the mixed problem for symmetric hyperbolic systems, Trans. Amer. Math. Soc. 168, 165–188 (1972).

   Google Scholar 

Download references