A SEMILINEAR PARABOLIC-SYSTEM IN A BOUNDED DOMAIN
A SEMILINEAR PARABOLIC-SYSTEM IN A BOUNDED DOMAIN
复制标题
DOI：
10.1007/bf01765854
复制
发表时间：
1993-01-01
影响因子：
1
通讯作者：
HERRERO, MA
中科院分区：
文献类型：
--
作者：
ESCOBEDO, M;HERRERO, MA
当omega是R(N)中边界光滑的有界开域，p和q为正参数，函数u0(X)，v0(X)连续、非负且有界时，考虑系统[图形]。很容易证明(S)有一个非负经典解定义在某个柱面Q(T)=(0，T)x欧米伽中，其中T小于或等于无穷大。我们证明了如果Pq大于或等于1，或者当初始函数u0，v0不同于零时，解实际上是唯一的。在最后一种情况下，我们刻画了从初值(u0，v0)=(0，0)产生的全部解的集合。当0<；pq小于或等于1时，每一个解都存在，但如果pq>；1，则解可能是全局的，或者根据初值(u0，v0)的大小在有限时间内爆破。
Consider the system [GRAPHICS]when OMEGA is a bounded open domain in R(N) with smooth boundary, p and q are positive parameters, and functions u0(x), v0(x) are continuous, nonnegative and bounded. It is easy to show that (S) has a nonnegative classical solution defined in some cylinder Q(T) = (0, T) x OMEGA with T less-than-or-equal-to infinity. We prove here that solutions are actually unique if pq greater-than-or-equal-to 1, or if one of the initial functions u0, v0 is different from zero when 0 < pq < 1. In this last case, we characterize the whole set of solutions emanating from the initial value (u0, v0) = (0, 0). Every solution exists for all times if 0 < pq less-than-or-equal-to 1, but if pq > 1, solutions may be global or blow up in finite time, according to the size of the initial value (u0, v0).