一类色散耗散波动方程的整体强解

Strong solutions to a class of wave equations with dispersive-dissipative terms

对一类四阶非线性色散、耗散波动方程的初边值问题进行研究.在非线性项和初值满足一定条件的前提下,利用位势井方法得到其整体强解的存在性,并给出了问题解的某些集合在流之下的不变性.

The initial-boundary value problem for a class of nonlinear dispersive-dissipative wave equations of fourth order were studied. Under some conditions on the nonlinear term and the initial data, by the potential well argument we discuss the existence of global strong solutions and give the invarianee of some sets of the solutions to the problem under the flow.