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霍朝辉 《数学物理学报(B辑英文版)》2016,(4):1117-1152
The Cauchy problem of the Klein-Gordon-Zakharov equation in three dimensional space {utt-?u + u =-nu,(x, t) ∈ R~3× R_+,ntt-?n= ?|u|~2,(x, t) ∈ R~3× R_+,u(x, 0) = u_0(x), ?_tu(x, 0) = u_1(x),n(x, 0) = n_0(x), ?_tn(x,0) =n_1(x),(0.1) is considered. It is shown that it is globally well-posed in energy space H~1× L~2× L~2× H~(-1) if small initial data(u_0(x), u_1(x), n_0(x), n_1(x)) ∈(H~1× L~2× L~2× H~(-1)). It answers an open problem: Is it globally well-posed in energy space H~1× L~2× L~2× H~(-1) for 3D Klein-GordonZakharov equation with small initial data [1, 2]? The method in this article combines the linear property of the equation( dispersive property) with nonlinear property of the equation(energy inequalities). We mainly extend the spaces F~s and N~s in one dimension [3] to higher dimension. 相似文献
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本文研究四阶Ginzburg-Landau型方程的初值问题,通过建立一般半线性抛物方程的Lr-解和Hs-解之间的联系,获得该方程的整体Hs-解的存在唯一性(s=1,2). 相似文献
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本文研究四阶Ginzburg-Landau型方程的初值问题,通过建立一般半线性抛物方程的Lτ-解和Hs-解之间的联系,获得该方程的整体Hs-解的存在唯一性(s=1、2)。 相似文献
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