Admissible Lp norms for local existence and for continuation in semilinear parabolic systems are not the same
Admissible Lp norms for local existence and for continuation in semilinear parabolic systems are not the same
复制标题
半线性抛物线系统中局部存在性和连续性的容许 Lp 范数不同
DOI：
10.1017/s0308210500001475
复制
发表时间：
2001
期刊：
影响因子：
--
通讯作者：
P. Souplet
中科院分区：
文献类型：
--
作者：
P. Quittner;P. Souplet
如果任何非全局解的E-范数必须变得无界，则我们说Banach空间E是给定抛物问题的连续空间。我们将证明，对于两个方程的抛物型方程组的大类，空间E = Lr 1 × Lr 2可以是连续空间，即使该问题在E中不是局部适定的。这与类似标量方程的经典结果相反。
We say that a Banach space E is a continuation space for a given parabolic problem if the E-norm of any non-global solution has to become unbounded. We will prove that for large classes of parabolic systems of two equations, the space E = Lr1 × Lr2 can be a continuation space even though the problem is not locally well posed in E. This stands in contrast with classical results for analogous scalar equations.