m-拉普拉斯型抛物方程解的有界支集

BOUNDED SUPPORT OF SOLUTIONS TO m-LAPLACE TYPE PARABOLIC EQUATIONS

本文研究了方程 u t=Δum- uq 具有初始条件 u( x,0 ) =u0 的 Cauchy问题解的局部化条件及解的全局熄灭问题 ,其中 m>1,q>0 .u0 是 RN中具有紧支集的有界非负连续函数 .本文的主要结果是 :如果 1<q<m,那么 supp u(· ,t) BL,其中L是与时间

A study of the localization conditions and global dieout of solutions of the Cauchy problem has been made whose prototype is ut=Δu m-u q with initial condition u(x,0)=u 0. Here m>1, q>0 ,u 0 is a bounded,non negative and continuous function with compact support in R N.Conclusion is drawn that if 1<q<m, then supp u(·,t)B L, in which L is a positive constant independent of time.