With Dissipation Term For First Order Quasilinear Hyperbolic Systems Of Global Smooth Solution

This paper first considers the initial value problem of the nonlinear damped p-system:It doesn't require that the C~0 - norm of the initial data is small, and just need the C~0 - norm ofthe first-order derivative is sufficiently small. Utilizing some a priori estimates, we prove the existences of the global smooth solutions for the initial value problem (1),(2) .In order to get a priori estimates of the solutions, the classical characteristic method, which is used to get the apriori C~0 -norm estimates on the solutions, and by applying the maximum principle to getuniformly estimates on the derivatives of the solutions with respect to x .In second part, the problem mentioned above is extended to the initial value problems of forced quasilinear wave equation with nonlinear dissipation:Using the same methods, we obtain also the similar results.