On the Cauchy problem with small analytic data for nonlinear weakly hyperbolic systems
The author investigates the Cauchy problem for first order nonlinear hyperbolic systems. By using the pseudo-differential operators of infinite order the hyperbolic systems are reduced to parabolic systems and the analytic solutions of the Cauchy problem for hyperbolic systems are obtained locally in time. Moreover, it is shown that the life span of the solutions tends to infinity together with the initial data decreasing to zero.
scientific article; zbMATH DE number 1102898