Global existence, large time behavior and life span of solutions of a semilinear parabolic cauchy problem
Global existence, large time behavior and life span of solutions of a semilinear parabolic cauchy problem
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DOI：
10.1090/s0002-9947-1992-1057781-6
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发表时间：
1992
影响因子：
1.3
通讯作者：
Tzong-Yow Lee;W. Ni
中科院分区：
文献类型：
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作者：
Tzong-Yow Lee;W. Ni
我们研究了(…)的解u(x，t)的性态。其中Δ=Σ1=1 n∂2/∂xi 2是拉普拉斯算子，p>；1是常数，T>；0，φ是Rn中的非负有界连续函数。主要结果是关于初值φ在x=∞附近有多项式衰减的情况。假设φ∼λ(1+|x|)#75a具有λ，a>；0，则利用λ，a，p和空间维度n上的简单条件，回答了解u(x，t)的整体(时间)存在和不存在、大时间性态或生命跨度的各种问题
We investigate the behavior of the solution u(x, t) of (...) where Δ = Σ 1=1 n ∂ 2 /∂ xi 2 is the Laplace operator, p > 1 is a constant, T > 0, and φ is a nonnegative bounded continuous function in R n . The main results are for the case when the initial value φ has polynomial decay near x = ∞. Assuming φ ∼ λ(1+|x|) #75a with λ, a > 0, various questions of global (in time) existence and nonexistence, large time behavior or life span of the solution u(x, t) are answered in terms of simple conditions on λ, a, p and the space dimension n