Critical exponents for the blow-up of solutions with sign changes in a semilinear parabolic equation
Critical exponents for the blow-up of solutions with sign changes in a semilinear parabolic equation
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DOI：
10.1007/s002080050055
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发表时间：
1997-04
影响因子：
1.4
通讯作者：
N. Mizoguchi;E. Yanagida
中科院分区：
文献类型：
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作者：
N. Mizoguchi;E. Yanagida
研究了Cauchy问题[公式]解的爆破。设Λ k是R上改变k次符号的函数的集合。证明了对pk =1+2/（k+1），k=0，1，2，.，当1<p <$pk时，任何满足u 0 ∈Λ k的解在有限时间内爆破，而当p>pk时，存在满足u 0 ∈Λ k的整体解.这是我们先前结果[17]的扩展，其中对初始数据施加了快速衰减条件。本文还表明，如果u_0的衰变速度慢于|X| −2/（p−1）作为|X| →+∞，则解在有限时间内爆破，与符号变化的次数无关。
The blowup of solutions of the Cauchy problem[formula]is studied. LetΛkbe the set of functions onRwhich change signktimes. It is shown that forpk=1+2/(k+1),k=0, 1, 2, …, any solution withu0∈Λkblows up in finite time if 1<p⩽pk, whereas a global solution withu0∈Λkexists ifp>pk. This is an extension of our previous result [17], in which a fast decay condition was imposed on initial data. It is also shown in this paper that if u0 decays more slowly than |x|−2/(p−1)as |x|→+∞, then the solution blows up in finite time regardless of the number of sign changes.