Complete blow up and global behaviour of solutions of ut - Δu = g(u)
Complete blow up and global behaviour of solutions of ut - Δu = g(u)
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ut - Δu = g(u) 解的完全爆炸和全局行为
DOI：
10.1016/s0294-1449(99)80002-x
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发表时间：
1998
影响因子：
1.9
通讯作者：
Y. Martel
中科院分区：
文献类型：
--
作者：
Y. Martel
对于u0∈L∞(ω), u0≥0，我们研究了非线性热方程(1)解的全局行为。定义域ω光滑且有界，非线性g是非负的、非递减的、凸的。我们特别证明了在有限时间Tmax爆炸的任何非递减解在Tmax之后完全爆炸。我们将这一结果应用于(1)的解根据λ值的所有可能的全局行为的描述。当我们引入在无限时间内完全爆炸的概念时，我们得到了类似的结果。
For u0∈ L∞(ω), u0≥ 0, we study the global behaviour of solutions of the nonlinear heat equation (1). The domain ω is smooth and bounded and the nonlinearity g is nonnegative, nondecreasing and convex. We show in particular that any nondecreasing solution blowing up at the finite time Tmaxblows up completely in ω after Tmax. We apply this result to the description of all possible global behaviours of the solutions of (1) according to the value of λ. We show similar results when we introduce a notion of complete blow up in infinite time.