We are concerned with classical solutions to the initial value problem for u = |u|p or u = |ut|p in Rn x [0, ∞) with "small" data. If the data have compact support, it is partially known that there is a critical number p0(n) such that most solutions blow-up in finite time for 1 < p ≤ p0(n) and a global solution exists for p > p0(n). In this paper, we shall show for all n ≥ 2 that, if the support of data is noncompact, there are blowing-up solutions even for p > p0(n) because of the "bad" spatial decay of the initial data. Moreover, critical decays for each equation are conjectured. The proof lies in the pointwise estimates of the fundamental solution of.
|Number of pages||15|
|Journal||Differential and Integral Equations|
|Publication status||Published - 1995 Jan 1|
ASJC Scopus subject areas
- Applied Mathematics