Large time behavior of solutions for the generalized Kadomtsev-Petviashvili equation
Large time behavior of solutions for the generalized Kadomtsev-Petviashvili equation
复制标题
广义 Kadomtsev-Petviashvili 方程解的大时间行为
DOI：
10.7153/dea-03-18
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发表时间：
2011
影响因子：
0.3
通讯作者：
T. Niizato
中科院分区：
文献类型：
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作者：
T. Niizato
考虑广义Kadomtsev-Petviashvili(KP)方程{ut+uxxx+σ∂−1xuyy=−(U)x，(x，y)∈R2，t∈R，u(0，x，y)=u0(x，y)，(x，y)∈R2的柯西问题，其中σ=1或σ=−1，∂−1x=∫x−∞dx‘.Hayashi-Naumkin-Saut[2]证明了当ρ_3和初值足够小且规则时，KP方程解的渐近性。我们的目的是填补[2]中L∞小解时间衰减证明的空白，改进他们关于数据正则性的结果。数学学科分类(2010)：35Q53。
We consider the Cauchy problem for the generalized Kadomtsev-Petviashvili (KP) equation { ut +uxxx +σ∂−1 x uyy = −(u)x, (x,y) ∈ R2, t ∈ R, u(0,x,y) = u0(x,y), (x,y) ∈ R2, where σ = 1 or σ = −1 , ∂−1 x = ∫ x −∞ dx′ . Hayashi-Naumkin-Saut [2] have shown asymptotics of solutions for KP equation when ρ 3 and the initial data is sufficiently small and regular. Our aim is to fill the gap of the proof of L∞ time decay of small solutions obtained in [2] and improve their result on the regularity of the data. Mathematics subject classification (2010): 35Q53.