摘要
本文考虑一类描述在某种介质中传播且具耗散的声波方程的初边值问题，利用Ｇａｌｅｒｋｉｎ方法结合能量估计在初值及非齐次项满足适当的条件下，证明了问题存在唯一整体解。最后还讨论了当非齐次项是周期函数时，所述问题周期解的存在性。
This paper discusses the initial and boundary value problem for an equation that describes acoustic waves in a medium with dispersion. By using the Galerkin's methods and the estimate of energy, we have proved that there exists a unique global solution to the problem when the initial value and nonhomogeneous term satisfy suitable conditions. At the end of the paper we have proved that there exists a periodic solution to the problem when the nonhomogenous term is a periodic solution.
出处
《兰州大学学报（自然科学版）》
CAS
CSCD
北大核心
1994年第1期5-10,共6页
Journal of Lanzhou University(Natural Sciences)
关键词
耗散
初边值问题
声波方程
Galerkin's method
energy integrals
periodic solution
acoustic wave equation
global solution
