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61.
本文应用Normal Form理论和退化向量场的普适开折理论研究了参数激励与强迫激励联合作用下非线性振动系统的余维2退化分叉,用Melnikov方法讨论了全局分叉的存在性. 相似文献
62.
非线性动力系统的规范形和余维3退化分叉 总被引:3,自引:0,他引:3
本文里我们利用矩阵表示法计算了具有Z_(2~-)对称性时非线性动力系统的高阶规范形,求出了余维2退化和余维3退化情况下相应规范形的普适开折。最后利用所得到的规范形和普适开折讨论了非线性动力系统的余维3退化分叉。 相似文献
63.
B. Visser M. Beck P. Bornhauser G. Knopp T. Gerber R. Abela J. A. van Bokhoven P. P. Radi 《Journal of Raman spectroscopy : JRS》2016,47(4):425-431
The potential of two‐color resonant and degenerate four‐wave mixing spectroscopy for investigations of the complex spectra of transition metal dimers is explored. Two‐color resonant and degenerate four‐wave mixing spectroscopy scans of the well‐known A‐X and B‐X transitions in Cu2 are reported and compared with previous experimental data obtained from standard single‐resonance techniques. The selectivity of the method is shown to enable the measurement of isotopologue pure spectra without the need for isotopically enriched metal targets. Specific subsets of the rovibronic structure are separated in a congested spectral region of overlapping transitions. The sensitivity of the method compares satisfactorily with linear spectroscopic methods such as laser‐induced fluorescence and cavity ring‐down. A new laser vaporization source for the production of transition metal dimers and clusters has been constructed. The new design aims for a high number density and maximum possible shot‐to‐shot stability. The possibilities of further applications of non‐linear four‐wave mixing spectroscopy to Cu2 and other transition metal dimers are discussed. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
64.
参数激励与强迫激励联合作用下非线性振动系统的余维2退化分叉 总被引:4,自引:0,他引:4
在本文里我们首先研究了具有Z_2-对称性的范式理论和退化向量场的普适开折理论。然后利用上述理论研究了参数激励与强迫激励联合作用下非线性振动系统的余维2退化分叉,从而解决了当解具有两个零特征值时解的稳定性问题。最后利用Melnikov方法求出了参数平面上的同宿分叉曲线,讨论了全局分叉的存在性。 相似文献
65.
The nonlinear propagation of modified electron‐acoustic (mEA) shock waves in an unmagnetized, collisionless, relativistic, degenerate quantum plasma (containing non‐relativistic degenerate inertial cold electrons, both nonrelativistic and ultra‐relativistic degenerate hot electron and inertial positron fluids, and positively charged static ions) has been investigated theoretically. The well‐known Burgers type equation has been derived for both planar and nonplanar geometry by employing the reductive perturbation method. The shock wave solution has also been obtained and numerically analyzed. It has been observed that the mEA shock waves are significantly modified due to the effects of degenerate pressure and other plasma parameters arised in this investigation. The properties of planar Burgers shocks are quite different from those of nonplanar Burgers shocks. The basic features and the underlying physics of shock waves, which are relevant to some astrophysical compact objects (viz. non‐rotating white dwarfs, neutron stars, etc.), are briefly discussed. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
66.
Global existence and blow-up solutions for doubly degenerate parabolic system with nonlocal source 总被引:1,自引:0,他引:1
Jian Wang 《Journal of Mathematical Analysis and Applications》2011,374(1):290-310
This paper deals with the following nonlocal doubly degenerate parabolic system
67.
Kazuaki Taira 《Mathematische Nachrichten》2011,284(1):105-123
The purpose of this paper is to study a class of semilinear elliptic boundary value problems with degenerate boundary conditions which include as particular cases the Dirichlet problem and the Robin problem. The approach here is based on the super‐sub‐solution method in the degenerate case, and is distinguished by the extensive use of an Lp Schauder theory elaborated for second‐order, elliptic differential operators with discontinuous zero‐th order term. By using Schauder's fixed point theorem, we prove that the existence of an ordered pair of sub‐ and supersolutions of our problem implies the existence of a solution of the problem. The results extend an earlier theorem due to Kazdan and Warner to the degenerate case. © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim 相似文献
68.
Stefanie Sonner Messoud A. Efendiev Hermann J. Eberl 《Mathematical Methods in the Applied Sciences》2011,34(13):1667-1684
We analyze a system of reaction–diffusion equations that models quorum‐sensing in a growing biofilm. The model comprises two nonlinear diffusion effects: a porous medium‐type degeneracy and super diffusion. We prove the well‐posedness of the model. In particular, we present for the first time a uniqueness result for this type of problem. Moreover, we illustrate the behavior of model solutions in numerical simulations. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
69.
吴斌 《数学物理学报(B辑英文版)》2011,31(3):960-968
In this paper, we consider a degenerate steady-state drift-diffusion model for semiconductors. The pressure function used in this paper is ()(s) = s~α(α > 1). We present existence results for general nonlinear diffhsivities for the degenerate Dirichlet-Neumann mixed boundary value problem. 相似文献
70.