一类高阶发展方程初值问题的局部解及其一个性质

Local Solution of the Initial Value Problem for a Class of High Order Evolution Equations

本文研究了一类高阶非线性发展方程的初值问题(正文问题(p)).在较广泛的限制条件下,利用抽象发展方程的理论,得到了初值问题的局部解在某sobolev空间中的适定性.并证明了(定理2.2)当初值的正则性有变化时初值问题具有固定不变的局部解存在区间的结论.即局部解的存在区间不与初值的正则性的变化而缩小,从而为整体解的研究提供了有利条件(见定理2.3).

We study the following initial value problem for a class of high order nonlinear evolution equations Using abstract evolution equation theory,we show that under rather general restrictions the local solution of (p) is well-posed in a certain Sobolev space.It is showed(theorm2.2) that the existence interval of the local solution will not shrink with the variation of regularities of the initial values,the latter property is useful in the study of the Global solution(theorem2.3).