Global existence and smoothing effect for the complex Ginzburg-Landau equation with p-Laplacian
Global existence and smoothing effect for the complex Ginzburg-Landau equation with p-Laplacian
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DOI：
10.1006/jdeq.2001.4097
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发表时间：
2002-07
影响因子：
2.4
通讯作者：
N. Okazawa;T. Yokota
中科院分区：
文献类型：
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作者：
N. Okazawa;T. Yokota
1 p和u是一个复值未知函数，Dpu：¼ divšjrujp然而，我们不能将半线性理论，例如相应积分方程的压缩方法，应用于p> 2的<$CGLLP：因此，似乎没有关于<$CGLLP的前期工作：为了克服困难，我们开发了复空间版本的单调性方法，其中凸函数的次微分起着核心作用。这解释了从<$CGL2到<$CGLp的推广：单调性方法至少在真实的空间中是独立于空间维度N的。证明了维数无关性在复空间中也成立。我们已经在以前的论文[8]中对šCGL 2进行了这种类型的考虑，
Ą1 p and u is a complex-valued unknown function with Dpu: ¼ divšjrujpĄ2ruŽ; p; q 2 ½2; 1Ž: In particular, šCGLŽ2 is a problem for the usual complex Ginzburg–Landau equation and recently studied very extensively (see eg [3–5, 15]). However, one cannot apply the semilinear theory, such as contraction methods for the corresponding integral equation, to šCGLŽp with p> 2: Therefore, there seems to be no preceding work on šCGLŽp: To overcome the difficulty, we develop the complex space version of monotonicity methods in which subdifferentials of convex functions play the central role. This accounts for the generalization from šCGLŽ2 to šCGLŽp: Monotonicity methods are known to be independent of spatial dimension N at least in real spaces. The dimension independence is proved to be true also in complex spaces. We have already carried out this type of consideration for šCGLŽ2 in a previous paper [8] under the strict restriction on the complex