非线性色散方程的初边值问题

Initial boundary problem of nonlinear dispersive equations

针对一类四阶具有色散效应的一维弹性杆的非线性纵向波动方程的初边值问题,借助Sobolev空间、紧性原理和利用Galerkin方法,解决了此类方程整体广义解存在性和惟一性,在此基础上,又处理了整体古典解的存在性和惟一性.所得结果为解决类似方程的其他问题提供了理论基础.

Initial boundary value problems and a class of forth order nonlinear wave equations of longitudinal vibration of the 1-D elastic rod with dispersive effect are studied.Firstly,by using of Galerkin method,Sobolev space and compacts principle,the existence and uniqueness of global general solutions are solved.On the basis the existence and uniqueness of global classic solutions are dealt with.The theorem foundations can be supplied to other solving on similar equations.