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张晓轶 《数学物理学报(A辑)》2005,25(5):652-662
该文证明了复Ginzburg Landau方程在非标准的函数空间X_{s,p}中整体解的存在唯一性;考察了其解在X_{0,α+2}中的极限行为,得到当参数ε→0++或a→0, ε→0++时,Ginzburg Landau方程的解关于时间一致收敛到相应极限方程的解 相似文献
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研究了具有非线性项|u|~αu的半线性波动方程的Cauclly问题,利用仿积分解及交换子估计等技术,证明了当α为一般的实数且满足一定的限制时,Cauchy问题自相似解的存在性。本文的结果回答了Planchon在其工作中所遗留的问题。 相似文献
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In this paper we consider the Cauchy problem to the following semi-linear Schrdinger equation 相似文献
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The usual Kato smoothing estimate for the Schrodinger propagator in 1D takes the form |||δx|1/2eitθxxu0|| Lx∞Lt2〈∽||u0||Lx2. In dimensions n ≥ 2 the smoothing estimate involves certain localization to cubes in space. In this paper we focus on radial functions and obtain Kato-type sharp smoothing estimates which can be viewed as natural generalizations of the 1D Kato smoothing. These estimates are global in the sense that they do not need localization in space. We also present an interesting counterexample which shows that even though the time-global inhomogeneons Kato smoothing holds true, the corresponding time-local inhomogeneous smoothing estimate cannot hold in general. 相似文献
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