On Nonexistence of Global Solutions of Some Semilinear Parabolic Differential Equations
On Nonexistence of Global Solutions of Some Semilinear Parabolic Differential Equations
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DOI：
10.3792/pja/1195519254
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发表时间：
1973
期刊：
影响因子：
--
通讯作者：
K. Hayakawa
中科院分区：
文献类型：
--
作者：
K. Hayakawa
本文证明了半线性抛物型方程（a/3 t）u-zlu +u对任意非平凡非负初值Uo（X）在N-2，a-1或N=I，a-2的情形下没有整体解，其中N表示x-空间的维数. Fujita H. [1]更一般的形式[2]。[1]的结论如下。在Na 2的情况下，对于任何非平凡的非负初始数据都不存在全局解。另一方面，在Na 2的情况下，存在足够小的初始数据的全局解，并且没有足够大的初始数据的全局解。本文将对Na-2案作部分解决。我们考虑下一个问题。
The purpose of this paper is to show that the semilinear parabolic equation (a/3t)u--zlu+u has no global solutions for any nontrivial nonnegative initial data Uo(X) in case of N--2, a--1 or N=I, a--2, where N denotes the dimension of x-space. This problem was considered in Fujita H. [1] and in more general form [2]. The conclusions of [1] are as follows. In case of Na2 there does not exist a global solution for any nontrivial nonnegative initial data. On the other hand, in case of Na2, there exists a global solution for sufficiently small initial data, and no global solutions for sufficiently large initial data. This paper will give a partial settlement for the case Na--2. We consider the next problem.