强阻尼非线性波动方程U_（tt）－△U－V△U_t＝F（△u，△x△u，△u_

Cauchy Ptoblem for Strongly Damped Nonlinear Wave Equations

本文讨论了方程Ｕｕ－△ｕ－ｖ△Ｕｔ＝Ｆ（ｕ，ｘｕ，△ｕｔ）的初值问题，幂性非线性项Ｆ（）＝ａ＞１为整数，及空间维数的条件下，论证了小初值问题在时间大范围的可解性、唯一性，方法基于线性方程解的衰减估计和能量估计所设计的某种度量空间上的压缩映象原理。

e consider the Cauchy problem for the equationsUnder the assumptions of ,With integral number a>1 and space dimension n>the global existence and uniqueness of the solution to the equation with small initial values are obtained.The proof is achieved by using contracting mapping principle on the metric spacethat is designed by energy estimates and decay estimates of the linear equations.