一类波动方程解的导数损失

Loss of derivatives on a class of wave equations

研究了一类变系数波动方程的柯西问题的导数损失情况,运用Gronwall不等式建立了关于能量泛函的估计,最终得到波动方程解的导数损失是有限的,并举出实例加以说明.

The paper studies the Cauchy problem for wave equations with variable coefficients in the time variable.Under some appropriate conditions on the coefficients a（t）,by establishing the estimates of the energy functional,the loss of derivatives to the solution for the Cauchy problem is obtained.An application is also provided.