一类非线性波动方程解的性质

Property of Solution to a Nonlinear Wave Equation

研究了一类具有线性阻尼和非线性源项的变系数波动方程Cauchy问题,由于这个非线性问题的显式解求不出来,因此对解的性质的讨论就很必要.利用凸性方法证明了初值、源项的增长阶数在一定的条件下解在有限时刻发生爆破,利用能量扰动法证明了在一定条件下解是整体存在的.

A class of Cauchy problem of wave equations with varying coefficients,linear damping and nonlinear source term was discussed.Since the explicit solution of the problem can not be solved,the discussion to the property of the solution is important.By using convexity method,the blow-up solution within finite time was proved that if initial values,the damping and the growth of source term are under certain conditions.With energy perturbation method,the global existence of the solution was proved that if initial values,the damping and the growth of source term are under certain conditions.