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81.
82.
We consider the flow of an inviscid nonheatconducting gas in the thermodynamical equilibrium state around a plane infinite wedge and study the stationary solution to this problem, the so-called strong shock wave; the flow behind the shock front is subsonic.We find a solution to a mixed problem for a linear analog of the initial problem, prove that the solution trace on the shock wave is the superposition of direct and reflected waves, and, the main point, justify the Lyapunov asymptotical stability of the strong shock wave provided that the angle at the wedge vertex is small, the uniform Lopatinsky condition is fulfilled, the initial data have a compact support, and the solvability conditions take place if needed (their number depends on the class in which the generalized solution is found). 相似文献
83.
Vladimir I. Ryazanov Matti K. Vuorinen 《Proceedings of the American Mathematical Society》2001,129(10):3049-3056
The local behavior of plane quasiconformal mappings is investigated. In particular, generalizing the well-known Reich-Walczak problem, we study the possibility for a quasiconformal mapping to be conformal in the sense of Belinskii at a prescribed point or in a prescribed set of points when the modulus of the complex dilatation is a fixed measurable function. The notion of the Belinskii conformality is related to the conception of asymptotical rotations by Brakalova and Jenkins.
84.
Arnak S. Dalalyan Yury A. Kutoyants 《Statistical Inference for Stochastic Processes》2003,6(1):89-107
The problem of estimation of the derivative of the invariant density is considered for a one-dimensional ergodic diffusion process. The lower minimax bound on the L
2-type risk of all estimators is proposed and an asymptotically efficient (up to the constant) in the sense of this bound kernel-type estimator is constructed. 相似文献
85.
86.
This article proposes a diffused hepatitis B virus (HBV) model with CTL immune response and nonlinear incidence for the control of viral infections. By means of different Lyapunov functions, the global asymptotical properties of the viral-free equilibrium and immune-free equilibrium of the model are obtained. Global stability of the positive equilibrium of the model is also considered. The results show that the free diffusion of the virus has no effect on the global stability of such HBV infection problem with Neumann homogeneous boundary conditions. 相似文献
87.
ZENG Ding-Fang 《理论物理通讯》2013,60(4):465-470
It is well known that confinings and asymptotic freedom are properties of quantum chromo-dynamics (QCD). But hints of these features can also be observed at purely classic levels. For this purpose we need to find solutions to the colorly-sourceful Yang-Mills equations with both confining and asymptotic freedom features. We provide such a solution in this paper which at the near-source region is of serial form, while at the far-away region is approximately expressed through simple elementary functions. From the solution, we derive out a classically non-perturbative beta function describing the running of effective coupling constant, which is linear in the couplings both in the infrared and ultraviolet region. 相似文献
88.
Hui Cao Xiaoyan Gao Dongxue Yan Suxia Zhang 《Mathematical Methods in the Applied Sciences》2020,43(6):3807-3826
This paper deals with the global dynamics for a tuberculosis transmission model with age-structure and relapse. The time delay in the progression from the latent individuals to becoming the infectious individuals is also considered in our model. We perform some rigorous analyses for the model, including presenting an explicit formula for the basic reproduction number of the model, addressing the persistence of the solution semiflow and the existence of a global attractor. Based on these analyses, we establish some results about stability and instability of the solutions for our model. At end, the model is applied to describe tuberculosis transmission in China. The number of the total population and the number of the annual newly reported TB cases both match the statistical data well. The number of the total population, the latent individuals, the infectious individuals, the Purified Protein Derivative (PPD) positive rate, and the prevalence rate from 2020 to 2035 all are presented. 相似文献
89.
运用类比法,构造了一类四阶非线性系统的李雅普诺夫函数,得到其平凡解全局渐近稳定的充分性准则,推广并改进了有关这类系统的其它结果. 相似文献
90.
In this paper the stability of nonlinear nonautonomous systems under the frequently-acting perturbation is studied.This study is a forward development of the study of thestability in the Liapunov sense;furthermore,it is of significance in practice sinceperturbations are often not single in the time domain.Malk in proved a general theoremabout thesubject.To apply the theorem,however,the user has to construct a Liapunovfunction which satisfies specified conditions and it is difficult to find such a function fornonlinear nonautonomous systems.In the light of the principle of Liapunov’s indirectmethod,which is an effective method to decide the stability of nonlinear systems in theLiapunov sense,the authors have achieved several important conclusions expressed in theform of theorems to determine the stability of nonlinear nonautonomous systems under thefrequently-acting perturbation. 相似文献