一类非线性蜕化抛物型方程组全局解的存在性和衰减性

EXISTENCE AND DECAY OF GLOBAL SOLUTION OF ANONLINEAR DEGENERATED PARABOLIC EOUATION SYSTEM

主要考虑（Ｅ１）全局解的存在性和衰减性。在（Ｅ１）的假设下，证明了：α＿（ｉｊ）＜ｐ＿ｉ－１问题（Ｅ１）存在一个全局解以Ｕ（ｘ，ｔ）。α＿（ｉｊ）＞ｐ＿ｉ－１（ｉ，ｊ＝１，ｍ）；那么，存在ｄ＿０＞０，使得如，问题（Ｅ１）存在一个全局解以ｕ（ｘ，ｔ）．

This paper deals mainly with the problem of existence and decay of the global so-lution of a nonlinear degenerated parabolic equation system. The main results are: if α_(ij) <p_iand(E1)admits a global solution u(x,t),and if α_(ij)and there exists d>0 such that the problem(E1)admits a global solution u(x.t).which satisfies where p=min{p}