一类四阶非线性波动方程的初边值问题

Initial Boundary Value Problem for a Class of Fourth Order Nonlinear Evolution Equations

本文研究一类描述非线性粘弹性杆中纵波振动的非线性波动方程的初边值问题 ,用 Galerkin方法证明了其整体强解的存在性、唯一性 .

In this paper, the initial boundary value problem for a class of fourth order no nli near evolution equations describing longitudinal wave vibration of a finite elas tic rod are studied. The existence, uniqueness of global strong solution for the problem are obtained by means of the Galerkin method, the asymptotic behavior a nd “blow up” phenomenon of the solution for the problem are discussed under ce rtain conditions.