共查询到20条相似文献，搜索用时 15 毫秒
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Global Existence of Solutions for the Kawahara Equation in Sobolev Spaces of Negative Indices 总被引：1，自引：0，他引：1
Hua WANG Shang Bin CUI Dong Gao DENG 《数学学报(英文版)》2007,23(8):1435-1446
We first prove that the Cauchy problem of the Kawahara equation, δtu ＋ uδxu ＋βδx^3u＋γδx^5u = 0, is locally solvable if the initial data belong to H^r（R） and r〉 r≥-7/5, thus improving the known local well-posedness result of this equation. Next we use this local result and the method of ＂almost conservation law＂ to prove that global solutions exist if the initial data belong to H^r（R） and r〉-1/2. 相似文献
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In this work we prove that the initial value problem of the Benney-Lin equation ut ＋ uxxx ＋ β（uxx ＋ u xxxx） ＋ ηuxxxxx ＋ uux = 0 （x ∈ R, t ≥0 0）, where β 〉 0 and η∈R, is locally well-posed in Sobolev spaces HS（R） for s ≥ -7/5. The method we use to prove this result is the bilinear estimate method initiated by Bourgain. 相似文献
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Min Jie SHAN 《数学学报(英文版)》1985,36(9):969-1000
The initial value problem for two-dimensional Zakharov-Kuznetsov equation is shown to be globally well-posed in Hs(R2) for all 5/7 < s < 1 via using I-method in the context of atomic spaces. By means of the increment of modified energy, the existence of global attractor for the weakly damped, forced Zakharov-Kuznetsov equation is also established in Hs(R2) for 10/11 < s < 1. 相似文献
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Xin Jun Gao 《数学学报(英文版)》2018,34(6):1015-1027
We prove the global well-posedness for the Cauchy problem of fifth-order modified Korteweg–de Vries equation in Sobolev spaces H~s(R) for s-(3/(22)).The main approach is the\"I-method\"together with the multilinear multiplier analysis. 相似文献
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讨论推广的海底取油管振动方程的初边值问题和初值问题解的整体不存在性,对初边值问题推广了Gmira和Guedda得到的结果,对初值问题的结果是新的. 相似文献
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We first define the pseudo almost periodic functions in a more general setting.Then we show the existence,uniqueness and stability of pseudo almost periodic solutions of parabolic inverse problems for a type of boundary value problems. 相似文献
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具有阻尼项的非线性波动方程的初值问题 总被引：2，自引：0，他引：2
本文研究具有阻尼项的非线性波动方程的初值问题ｕｔｔ－２ｂｕｘｘｔ＋ａｕｘｘｘｘ＝β（ｕｘ＾ｎ）ｘ,;ｕ（ｘ,０）＝ψ（ｘ）,ｕｔ（ｘ,０）＝ψ（ｘ）,其中ｂ〉０,β≠０为任意实数,ｎ≥２为整 当ａ≠ｂ＾２,ψ∈Ｌ１（Ｒ）∩Ｈ＾２（Ｒ）,ψ∈Ｋ１（Ｒ）∩Ｌ３（Ｒ）时,上述问题存在唯一的整体光滑解。 相似文献
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Boussinesq型方程的周期边界问题与初值问题的解的存在性 总被引：6，自引：0，他引：6
本文研究“坏的Ｂｏｕｓｓｉｎｅｓｑ型方程ｕｔｔ－ｂｕｘｘｘ＝σ（ｕ）ｘｘ的周期边界问题与初值问题的解的存在性问题,其中ｂ〉０为常数,证明了在相当宽松的条件下,上述问题存在局部广义解。 相似文献
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利用微分不等式和解的延拓原理,研究了一类带非线性阻尼和源项的耦合非线性波动方程,通过分析方程中参数的关系,得到了全局解存在的一些新的充分条件. 相似文献
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In this paper, we study the Cauchy problem for a viscous shallow water system with Korteweg type in Sobolev spaces. We first establish the local well-posedness of the solution by using the Friedrich method and compactness arguments. Then, we prove the global existence of the solution to the system for the small initial data. 相似文献
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In this paper we prove that the initial value problem of the OST equation ut+uxxx+η(Hux+Huxxx)+uux=0 (x∈R, t?0), where η>0 and H denotes the usual Hilbert transformation, is locally well-posed in the Sobolev space Hs(R) when , and globally well-posed in Hs(R) when s?0. 相似文献
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The Boussinesq approximation, where the viscosity depends polynomially on the shear rate,finds more and more frequent use in geological practice. In this paper, we consider the periodic initial value problem and initial value problem for this modified Boussinesq approximation with the viscous part of the stress tensor τ^v = τ(e)- 2μΔe, where the nonlinear function τ(e) satisfies τ _{ij}(e)e_{ij} ≥ C|e|^p or τ_{ij}(e)e_{ij} ≥ C(|e|²+|e|^p). The existence, uniqueness and regularity of the weak solution is proved for p > frac{2n}{n + 2}. 相似文献
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带耗散的广义Camassa-Holm方程的吸引子 总被引：1，自引：0，他引：1
讨论了一类带耗散的广义Camassa-Holm方程．先将方程的解以及初始条件化为积分平均为零,然后建立与原问题相应的周期初值问题近似解的先验估计,由此得到原问题解的存在唯一性,并证明了在H^2per（Ω）中吸引子的存在性． 相似文献