一类非线性退化抛物方程解的性质

Nature of Solution to Non-linear Retrogressive Prejectile Equation

研究了方程aU／at二dt”－”具有初始条件以t，0）＝t。的CanN问题解的局部化条件及解的全局熄灭问题．其中＜＞l，叮＞0．no是护中具有紧支集的有界非负连续函数．得到的主要结果是：如果1＜q＜m，那么U卜，t）C凤，其中L是与时间t无关的正数；如果q＞m，对于每个正数R，都存在一个时刻t使得suppuG，t）n（才＼B。）是一个非空的集合，其中BR＝Zxllxl＜R；如果0＜q＜l，那么存在广＞。，使以x，t）在S（上为零，其中文一th（T”，ac）．

The localization conditions and total extinction of the solution to Cauchy problem with initial condition u(x, 0) = u0 for equation , in which m >1, q > 0. u0 are bounded non-negative continuous function with compact subset in RN, are studied with the following as main results: if 1 < q < m, then u(, t) BL. where L is positive irrelevant to time t; if q < m, for each positive R, there is a moment t to make suppu(,t) (RN \ BR) a non-empty set, where BR = {x ||x|< R}; if 0 < q < 1, then T > 0 to Make μ(x,t) zero above S, where .