Global existence of classical solution to the nonlinear wave equations. (Chinese. English summary) Zbl 0895.35066
Summary: The existence and uniqueness of a global classical solution to the Cauchy problem for the wave equation \(u_{tt}- \Delta u=F(u,Du)\) are proved. Moreover, the decay estimates for \(u,Du\) and \(D^2u\) are obtained, which are the same as the corresponding homogeneous equation.
MSC:
| 35L70 | Second-order nonlinear hyperbolic equations |
| 35L15 | Initial value problems for second-order hyperbolic equations |
