LANDAU–GINZBURG TYPE EQUATIONS IN THE SUBCRITICAL CASE
LANDAU–GINZBURG TYPE EQUATIONS IN THE SUBCRITICAL CASE
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DOI：
10.1142/s0219199703000872
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发表时间：
2003-02
影响因子：
1.6
通讯作者：
N. Hayashi;E. Kaikina;P. Naumkin
中科院分区：
文献类型：
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作者：
N. Hayashi;E. Kaikina;P. Naumkin
研究了非线性Landau-Ginzburg方程的Cauchy问题，其中α，β ∈ C，耗散条件<$α > 0.我们感兴趣的是亚临界情况。我们假设θ =| u0（x）dx|并且设初始数据u_0 ∈ L_1满足（1+ 1），|X|）au 0 ∈ L1，具有足够小的范数e =（1 +| X|）au 0 <$1，其中a ∈（0，1）.我们还假设σ足够接近。则存在柯西问题（*）的唯一解，使得对于大的t > 0，满足以下时间衰减估计。注意，与相应的线性情况相比，（*）的解的衰减速率更快。
We study the Cauchy problem for the nonlinear Landau–Ginzburg equation where α, β ∈ C with dissipation condition ℜα > 0. We are interested in the subcritical case . We assume that θ = | ∫ u0(x) dx| ≠ 0 and ℜδ (α, β) > 0, where Furthermore we suppose that the initial data u0 ∈ L1 are such that (1+|x|)au0 ∈ L1, with sufficiently small norm e = ‖(1 + |x|)a u0 ‖1, where a ∈ (0,1). Also we assume that σ is sufficiently close to . Then there exists a unique solution of the Cauchy problem (*) such that satisfying the following time decay estimates for large t > 0 Note that in comparison with the corresponding linear case the decay rate of the solutions of (*) is more rapid.