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1.
设H是域k上的Hopf代数。本文首先讨论了量子Yang-Baxter H-余模与Yang-Baxter方程的解的关系;然后作为应用,给出了任意Hopf代数上Yang-Baxter方程的一个解。  相似文献   

2.
RLW—Burgers方程的精确解   总被引:6,自引:0,他引:6  
王明亮 《应用数学》1995,8(1):51-55
借助未知函数的变换,RLW-Burgers方程和KdV-Burgers方程化为易于求解的齐次形式的方程,从而得到RLW-Burgers方程和KdV-Burgers方程的精确解。  相似文献   

3.
本文证明了非线性 Schrodinger方程的初边值问题的 Hs-解(1< s ≤ 2)的存在唯一性结果.  相似文献   

4.
尚亚东 《应用数学》2000,13(3):35-39
本文研究非线性Sobolev-Calpern方程的初边值问题整体解的不存性即解的爆破问题,用能量估计方法并借助于Jensen不等式证明了非线性Soboliv-Galpern方程各种初边值问题在某些假设下不存在整体解。  相似文献   

5.
杜殿楼  王鸿业 《应用数学》1998,11(3):98-102
本文推导出相联于HD(Harry-Dym)族的Lenard递归方程的多项式解,并证明了任一驻定HD方程的解都可由非线性比的HD特征值问题的解表示。  相似文献   

6.
本文给出Navier-Stokes方程某种边值问题局部解不唯一性的一个例证。  相似文献   

7.
本给出Navier-Stokes方程某种边值问题局部解不唯一性的一个例证。  相似文献   

8.
吴珞 《应用数学学报》1998,21(3):463-470
本文将证明Navier-Stokes方程的解当t→+∞时趋于稳态解,并由此推出N-S方程存在集合满足泛吸引子或函数不变集条件的充要条件。  相似文献   

9.
组合Zakharov-Kuznetsov方程的显式孤波解   总被引:5,自引:0,他引:5  
借助于Mathematica是吴消元法,本文通过用一个新的假设,获得了组合Za-kharov-Kuznetsov方程的12种孤波解,其中包括钟状与扭状组合型孤波解和周期型孤波解。这种假设也能用于其他的非线性演化方程(组)。  相似文献   

10.
本文对周期边界条件Navier-Stokes方程,证明了其Fourier非线性Galerkin逼近解的存在唯一性,同时给出了逼近解的误差估计.  相似文献   

11.
使用Pseudoparabolic正则化方法和从弱耗散Camassa-Holm方程自身导出的估计式,在Sobolev空间Hs(R)(s3/2)中,证明了该Camassa-Holm方程解的局部适定性.同时给出了一个在空间Hs(R)(1s2\3)中确保该方程弱解存在的充分条件.  相似文献   

12.
The local well-posedness of the Cauchy problem for the Hirota equation is established for low regularity data in Sobolev spaces Hs(s≥-1/4). Moreover, the global well-posedness for L2 data follows from the local well-posedness and the conserved quantity. For data in Hs(s > 0), the global well-posedness is also proved. The main idea is to use the generalized trilinear estimates, associated with the Fourier restriction norm method.  相似文献   

13.
王保祥 《数学进展》2000,29(5):421-424
本文证明了非线性Schrodinger方程的初值问题的H^S-解(1<s≤2)的存在唯一性结果。  相似文献   

14.
The nonlinear D-S equations on R^d, with general power nonlinearity and with both the focusing and defocusing signs, are proved to be ill-posed in the Sobolev space H^s whenever the exponent s is lower than that predicted by scaling or Galilean invariance, or when the regularity is too low to support distributional solutions. Authors analyze a class of solutions for which the zero-dispersion limit provides good approximations.  相似文献   

15.
This paper undertakes a systematic treatment of the low regularity local wellposedness and ill-posedness theory in Hs andHs for semilinear wave equations with polynomial nonlinearity in u and (e)u. This ill-posed result concerns the focusing type equations with nonlinearity on u and (e)tu.  相似文献   

16.
In this paper, we firstly define a decreasing sequence {P^n(S)} by the generation of the Sierpinski gasket where each P^n(S) can be obtained in finite steps. Then we prove that the Hausdorff measure H^8(S) of the Sierpinski gasket S can be approximated by {P^n(S)} with P^n(S)/(1 1/2^n-3)s ≤ H^8(S)≤ Pb(S).An algorithm is presented to get P^n(S) for n≤ 5. As an application, we obtain the best lower bound of H^8(S) till now: H^8(S) ≥ 0.5631.  相似文献   

17.
TheHAUSDORFFDIMENSIONANDMEASUREOFTHEGENERALIZEDMORANFRACTALSANDFOURIERSERIES¥RENFUThO;LIANGJINRONGAbstract:Thispaperstudiesth...  相似文献   

18.
设Sr是压缩比为r(0.250≤r≤0.292)的Sierpinski地毯,该文证明了Sr的Hausdorff测度满足公式:21-s/2≤Hs(Sr)≤2s/2,其中s=-logr4.  相似文献   

19.
In this paper we study the Cauchy problem for a class of semi-linear parabolic type equations withweak data n the homogeneous spaces.We give a method which can be used to construct local mild solutionsof the abstract Cauchy problem in C(σ,s,p)and L~q([O,T);H~(s,p)by introducing the concept of both admissiblequintuptet and compatible space and establishing estblishing time-space estimates for solutions to the linear parabolic typeequations For the small data,we prove that these results can be extended globally in time. We also study the  相似文献   

20.
This paper considers the following Cauchy problem for semilinear wave equations in n spacedimensions□φ = F( φ),φ(0, x) = f(x), tφ(0, x) = g(x),The minimal value of s is determined such that the above Cauchy problem is locally well-posed in Hs. It turns out that for the general equation s must satisfyThis is due to Ponce and Sideris (when n = 3) and Tataru (when n ≥ 5). The purpose of thispaper is to supplement with a proof in the case n = 2, 4.  相似文献   

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