Pointwise decay for the solutions of degenerate and singular parabolic equations
Pointwise decay for the solutions of degenerate and singular parabolic equations
复制标题
简并和奇异抛物线方程解的逐点衰减
DOI：
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发表时间：
2009
影响因子：
1.4
通讯作者：
P. Lindqvist
中科院分区：
文献类型：
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作者：
P. Juutinen;P. Lindqvist
本文研究了演化p-Laplace方程vt = div（|v| p−2 v），具有与时间无关的横向边界值。我们得到了maxx∈Ω的急剧衰减率|v（x，t）− u（x）|其中u是退化情形p > 2和奇异情形1 < p < 2的平稳解。证明中的一个关键工具是Moser迭代，它应用于差v（x，t）-u（x）。在奇异情况下，我们构造一个例子，证明著名的有限灭绝时间现象，当u ≥ 0时对v（x，t）有效，但对v（x，t）− u（x）没有对应的。
We study the asymptotic behavior, as t →∞, of the solutions to the evolutionary p-Laplace equation vt = div(|∇v|p−2∇v) with time-independent lateral boundary values. We obtain the sharp decay rate of maxx∈Ω|v(x, t)− u(x)|, where u is the stationary solution, both in the degenerate case p > 2 and in the singular case 1 < p < 2. A key tool in the proofs is the Moser iteration, which is applied to the difference v(x, t) − u(x). In the singular case we construct an example proving that the celebrated phenomenon of finite extinction time, valid for v(x, t) when u ≡ 0, does not have a counterpart for v(x, t)− u(x).