一类具周期源的退化抛物方程解的渐近性态

The Properties of a Degenerate Parabolic Equation with Periodic Source Term

讨论具周期源的退化抛物方程ut=Δum+θupsint的Cauchy问题解的几何性质以及解的传播性质,利用先验估计和比较原理,证明了在任意固定的时刻,解的扰动传播是有限的,并且得到了显示的表达式;证明了曲面Φ=[u(x,t)]mδ/q是随着时间t的连续变化而漂浮于空间RN+1中的完备黎曼流形,它与空间RN相切于低维流形Hu(t).

In this paper, the geometric and propagating properties of solution of the Cauchy problem for a degenerate parabolic equation ut=△um＋θupsint sint with periodic source term were discussed. The objective is to show that ： 1 ） the disturbance propagation of solution is limited ; 2） with continuous variation of time t, the surface φ=[u（x,t）]mδ/q is a complete Riemannian manifold floating in space RN N＋1 and is going to be tan- gent to the space RN at the boundary of the set of OHu （t） .