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1.
In this note,we provide a consistant thin layer theory for power law and Bingham incompressible fluids flowing down an inclined plane under the effect of gravity.The derivation of such equations is based on formal asymptotic expansions of solutions of Cauchy momentum equations in the shallow water scaling and in the neighbourhood of steady solutions so that we can close the average equations on the fluid height h and the total discharge rate q. 相似文献
2.
THE ASYMPTOTIC THEORY OF INITIAL VALUEPROBLEMS FOR SEMILINEAR WAVE EQUATIONS IN THREE SPACE DIMENSIONS 总被引:10,自引:0,他引:10
LAISHAOYONG MuCHUNLAI 《高校应用数学学报(英文版)》1997,12(3):321-332
This paper deals with the asymptotic theory of initial value problems for semilinear waveequations in three space dimensions. The well-posedness and validity of formal approximations ona long time scale of order |ε|^-1 are discussed in the classical sense of C^2 This result describes aceu-ratively the approximations of solutions. At the end of this paper an application of the asymptotictheory is given to analyze a special model for a perturbed wave equation, 相似文献
3.
In this paper, general functional equations of rooted essential maps on surfaces (orientable and nonorientable) are deduced and their formal solutions are presented. Further, three explicit for- mulae for counting essential maps on S2,N3 andN4 are given. In the same time, some known results can be derived. 相似文献
4.
In this article, cyclic codes and negacyclic codes over formal power series rings are studied. The structure of cyclic codes over this class of rings is given, and the relationship between these codes and cyclic codes over finite chain rings is obtained. Using an isomorphism between cyclic and negacyclic codes over formal power series rings, the structure of negacyclic codes over the formal power series rings is obtained. 相似文献
5.
In this paper we show how the simplest wave structure that balances compression and rarefaction in the nonlinear compressible Euler equations can be represented in a solution of the linearized compressible Euler equations. Such waves are exact solutions of the equations obtained by linearizing the compressible Euler equations about the periodic extension of two constant states separated by entropy jumps. Conditions on the states and the periods are derived which allow for the existence of solutions in the Fourier 1-mode. In [3, 4, 5] it is shown that these are the simplest linearized waves such that, for almost every period, they are isolated in the kernel of the linearized operator that imposes periodicity, and such that they perturb to nearby nonlinear solutions of the compressible Euler equations that balance compression and rarefaction along characteristics in the formal sense described in [3]. Their fundamental nature thus makes them of interest in their own right. 相似文献
6.
Medium logic (ML) is set up for the common theoritical foundation of the classical mathematics and fuzzy mathematics. It has been formalized as a new theory of logic. See note (1) and note (2). As mathematical logic the ML's construct reches the study of the informal deductive inference by means of studying the formal inference in it, and it demands the formal inference of ML reliable reflected the deductive inference. For this reason, this paper deals with its reliability. The result shows that the formal inference of M L consists with deductive inference, and that ML reliably reflects the deductive inference. 相似文献
7.
In this article,we consider the Lipschitz metric of conservative weak solutions for the rotation-Camassa-Holm equation.Based on defining a Finsler-type norm on the tangent space for solutions,we first establish the Lipschitz metric for smooth solutions,then by proving the generic regularity result,we extend this metric to general weak solutions. 相似文献
8.
Maria Schonbek 《数学物理学报(B辑英文版)》2011,31(6):2305-2312
In this paper we study a generalization of self-similar solutions. We show that just as for the solutions to the Navier-Stokes equations these supposedly singular solution reduce to the zero solution.In this paper we study a generalization of self-similar solutions. We show that just as for the solutions to the Navier-Stokes equations these supposedly singular solution reduce to the zero solution. 相似文献
9.
LiuYanyan WuJun 《分析论及其应用》2003,19(4):342-354
A set is called regular if its Hausdorff dimension and upper box-counting dimension coincide. In this paper, we prove that the random self-con formal set is regular almost surely. Also we determine the dimen-sions for a class of random self-con formal sets. 相似文献
10.
This paper is a continuation of [1]、[2]、[4]. In this paper, we shall con-tinue to constitute the formal theorems and the important substituting theorem(see theorem 16 in this paper) of the propositional calculus system of mediumlogic MP. The order numbers of following formal theorems follow those in reference[4] 相似文献
11.
Yasutaka Sibuya 《Journal of Differential Equations》2003,190(2):559-578
This paper is a continuation of the previous paper (J. Differential Equations 165 (2000) 255). The main subject is the Gevrey property of formal solutions of an analytic ordinary differential equation in powers of a parameter. In one case, a given formal solution itself is of the Gevrey type, while, in another case, the existence of a formal solution implies the existence of formal solutions of the Gevrey types. These situations are explained systematically in this paper. 相似文献
12.
在 Reid等人标准型概念的基础上 ,引进形式可积系统的概念 .并给出验证形式可积系统解的完备性的机械化算法 ,并用此方法证明了各向同性弹性力学方程组的胡海昌解的完备性问题 . 相似文献
13.
《Chaos, solitons, and fractals》2006,27(4):1026-1035
In this paper, a new generalized extended tanh-function method is presented for constructing soliton-like, period-form solutions of nonlinear evolution equations (NEEs). Compared with most of the existing tanh-function method, extended tanh-function method, the modified extended tanh-function method and generalized hyperbolic-function method, the proposed method is more powerful. By using this method, we not only can successfully recover the previously known formal solutions but also construct new and more general formal solutions for some NEEs. Make use of the method, we study the (3 + 1)-dimensional potential-YTSF equation and obtain rich new families of the exact solutions, including the non-travelling wave and coefficient functions’ soliton-like solutions, singular soliton-like solutions, periodic form solutions. 相似文献
14.
In this paper, some analytic approaches are formulated for the existence of analytic solutions of analytic nonlinear difference equations. From the point of view of dynamical systems, analytic solutions of such kinds of equations can be generally expressed by formal power series of exponential variables, so we are interested in considering a difference equation as a q-difference equation via a suitable coordinate transformation. After stating analytic results for formal series solutions of nonlinear q-difference equations, we also derive some results for the existence of analytic solutions to autonomous rational difference equations. 相似文献
15.
Explicit solutions of generalized Cauchy-Riemann systems using the transplant operator 总被引:1,自引:0,他引:1
Vladislav V. Kravchenko 《Journal of Mathematical Analysis and Applications》2010,370(1):242-427
In Kravchenko (2008) [8] it was shown that the tool introduced there and called the transplant operator transforms solutions of one Vekua equation into solutions of another Vekua equation, related to the first via a Schrödinger equation. In this paper we prove a fundamental property of this operator: it preserves the order of zeros and poles of generalized analytic functions and transforms formal powers of the first Vekua equation into formal powers of the same order for the second Vekua equation. This property allows us to obtain positive formal powers and a generating sequence of a “complicated” Vekua equation from positive formal powers and a generating sequence of a “simpler” Vekua equation. Similar results are obtained regarding the construction of Cauchy kernels. Elliptic and hyperbolic pseudoanalytic function theories are considered and examples are given to illustrate the procedure. 相似文献
16.
G. K. Immink 《Journal of Difference Equations and Applications》2013,19(7):769-776
We prove a Maillet type theorem for formal solutions of nonlinear difference systems, relating the Gevrey order of the formal solutions to the lowest level of an associated, linear difference operator. 相似文献
17.
18.
Zhang Ping 《Applied mathematics and computation》2010,217(4):1688-1696
In this paper, by using the improved Riccati equations method, we obtain several types of exact traveling wave solutions of breaking soliton equations and Whitham-Broer-Kaup equations. These explicit exact solutions contain solitary wave solutions, periodic wave solutions and the combined formal solitary wave solutions. The method employed here can also be applied to solve more nonlinear evolution equations. 相似文献
19.
Recently the unified method for finding traveling wave solutions of nonlinear evolution equations was proposed by one of the authors. It was shown that, this method unifies all the methods being used to find these solutions. In this paper, we extend this method to find a class of formal exact solutions to Korteweg-de Vries equation with space-time dependent coefficients. 相似文献
20.
研究了一类含双参数的非线性高阶微分方程的奇摄动问题.运用合成展开法构造了问题的形式渐近解,并运用微分不等式理论证明了原问题解的存在性及所得形式渐近解的一致有效性. 相似文献