一类五阶色散波方程解的平均性质

The Average Property of a Fifth Order Dispersive Equation

研究了一类五阶色散波方程的Cauchy问题。通过估计方程的基本解确定的振荡积分,利用控制收敛定理,Riemann-Lebesgue定理等研究了基本解的衰减性,证明这类方程的解具有积分平均性质。

In this paper,we study the Cauchy problem of a fifth order dispersive equation.We estimate the oscillatory integral determined by the fundamental solution of this equation.By use of dominated convergence theorem and Riemann-Lebesgue theorem,we study the decay of fundamental solution and prove the integral average properly for the solution of this equation.