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1.
  总被引:1,自引:0,他引:1  
The solutions of the one-dimensional (1D) steady compressible Navier-Stokes equations have been thoroughly discussed before, but restrained for uniform total enthalpy, which leads to only a shock wave profile possible in an infinite domain. To date, very little progress has been made for the case with nonuniform total enthalpy. In this paper, we affirm that under nonuniform total enthalpy, there also exists steady solution for the 1D compressible Navier-Stokes equations, but the flow domain must be finite in the positive x-axis. The 1D steady compressible Navier-Stokes equations can be reduced to a singular perturbed nonlinear ordinary differential equation (ODE) for velocity with the assumptions of ◂=▸Pr=3/4 and a constant viscosity coefficient. By analyzing the mathematical property of the nonlinear ODE for velocity, we propose an asymptotic expansion for the solution of it as an exponential type sequence and also prove the convergence. Unlike the case of uniform total enthalpy, where the solutions for all variables keep monotone, we show that under nonuniform total enthalpy and some specific boundary conditions, there exists extreme inside the thin boundary layer. Numerical results verify the accuracy and convergence of the asymptotic expansion. This asymptotic expansion solution can serve as an important testing to demonstrate the efficiency of numerical methods developed for compressible Navier-Stokes equations at high Reynolds number.  相似文献   

2.
    
The exact solution of one-dimensional (1D) steady compressible Navier–Stokes (N-S) equations at high Reynolds number has not been given yet under nonuniform total enthalpy when the Prandtl number ( Pr $$ mathit{Pr} $$) is not equal to 0.75 since Becker's work in 1922. In this paper, we give an asymptotic expansion of the solution of the above equations at high Reynolds number by using the method of matched asymptotic expansions and prove convergence of the asymptotic solution under some assumptions. By analyzing the dimensionless form of one-dimensional steady compressible Navier–Stokes equations, we find that if there are extreme points inside the boundary layer, the number of extreme points of velocity is at most one more than that of total enthalpy and the extreme points of each flow variables are different from each other. Based on the second-order asymptotic expansion solution, we show that there are extreme points inside the thin boundary layer under some special conditions. Examples are given to verify theoretical analysis. The present asymptotic expansion solution is valuable for verifying the efficiency of high-order numerical methods in flow simulation of high Reynolds number.  相似文献   

3.
In this paper we study the existence of one-dimensional and multidimensional traveling wave solutions for general chemotaxis or so-called Keller-Segel models without reproduction of the chemotactic species. We present a constructive approach to give modelers a choice of chemotactic sensitivity functionals, production, and degradation terms for the chemical signal at hand. The main aim is to understand the type of functionals and the interplay between them that are needed for the traveling wave and pulse patterns to occur.  相似文献   

4.
    
In this paper, we investigate the asymptotic stability of a composite wave consisting of two traveling waves to a Keller–Segel chemotaxis model with logarithmic sensitivity and nonzero chemical diffusion. We show that the composite wave is asymptotically stable under general initial perturbation, which only be needed small in H1‐norm. This improves previous results. Copyright © 2017 John Wiley & Sons, Ltd.  相似文献   

5.
We show that any global-in-time bounded solution to the Keller-Segel chemotaxis model converges to a single equilibrium as time tends to infinity. The proof is based on a generalized version of the Lojasiewicz-Simon theorem.  相似文献   

6.
探讨泊松方程高次三角形有限元外推公式.为此先推导离散格林函数的权模估计和有限元解的渐近不等式展开,然后给出公式的证明.  相似文献   

7.
In this article, the globally bounded in-time pointwise estimate of solutions to the simplified Keller-Segel system modelling chemotaxis are derived. Moreover, a local existence theorem is obtained.  相似文献   

8.
ABSTRACT. In this article we discuss the asymptotic analysis of so‐called singularly perturbed differential equations. We begin by discussing some very simple nonmathematical examples, and then proceed to two mathematical examples, namely, the well‐known example of Friedrichs and a problem of John Mahony's. The presentation is addressed primarily to those who may have had little or no previous experience with this particular type of problem. However, the author hopes others will find something of interest in the somewhat unusual approach we take.  相似文献   

9.
The exterior boundary value problem of steady-state diffusion around a spherical particle placed in a Stokes flow is considered at high Peclet numbers. A complete asymptotic expansion of the solution in the wake of the particle is constructed by the method of matched asymptotic expansions.  相似文献   

10.
在二维空间中讨论了一个抛物-椭圆系统,而该系统来源于生物学中的趋化性模型.主要在Sobolev空间的框架下讨论了解的全局存在性与解的爆破性质,得出结论该系统存在一个门槛值,而该值决定了解全局存在或者发生爆破.最后利用利李亚普诺夫函数给出了定理的证明并得出结论.  相似文献   

11.
    
We consider the time-fractional Keller-Segel system of order α∈(0,1). Interesting properties of solutions are highlighted, like regularity and large time behavior in Lebesgue spaces, which depend on the fractional exponent α.  相似文献   

12.
In this paper we study quasi-neutral limit and the initial layer problem of the electro-diffusion model arising in electro-hydrodynamics which is the coupled Planck–Nernst–Poisson and Navier–Stokes equations. Different from other studies, we consider the physical case that the mobilities of the charges are different. For the generally smooth doping profile and for the ill-prepared initial data, under the assumption that the difference between the mobilities of two kinds of charges is very small, the quasi-neutral limit with an initial layer structure is rigorously proved by using the weighted energy method coupled with multi-scaling asymptotic expansions.  相似文献   

13.
讨论了一个非线性的抛物-椭圆系统,而该系统来源于生物数学中的一个趋化性模型.主要在Sobolev空间的框架下讨论了系统解的爆破性质,得出结论在二维空间中该系统存在一个门槛值,而该值决定了解全局存在或者是发生爆破.最后利用利亚普诺夫函数、下解爆破等方法给出了定理的证明并得出结论.  相似文献   

14.
An initial boundary value problem of semilinear nonlocal reaction diffusion equations is considered.Under some suitable conditions,using the asymptotic theory,the existence and asymptotic behavior of the interior layer solution to the initial boundary value problem are studied.  相似文献   

15.
Symmetric Stable Laws and Stable-Like Jump-Diffusions   总被引:7,自引:0,他引:7  
Asymptotic expansions are obtained for finite-dimensional symmetricstable distributions. They are used to prove the existence ofcontinuous transition probability densities of stable and stable-likejump-diffusions, and to construct local multiplicative asymptoticsandglobal two-sided estimates for these densities. As a consequence,the distribution of the first passage times for stable jump-diffusionsis estimated and the integral test for the limsup behaviourof their sample paths as t 0 is provided. 1991 MathematicsSubject Classification: 60E07, 60G17, 60J35, 47D07.  相似文献   

16.
    
In this paper, we analyze rigorously the asymptotic behaviors for perturbation of eigenvalues and eigenfunctions associated to the Stokes eigenvalue problem in the presence of a rapidly oscillating boundary. The aim is to construct asymptotic approximations, as δ⟶0$$ delta longrightarrow 0 $$, of the eigenvalues and corresponding eigenfunctions for the case where the eigenvalue of the reference problem is simple or multiple. Taking advantage of small oscillations, we use the method of matching of asymptotic expansions to construct the associated leading terms. We believe that our results are ambitious tools for determining shape and/or size of the small perturbed part of the domain by taking eigenvalue measurements.  相似文献   

17.
Fluid motion induced by the torsional oscillations (of angular velocity bΩcosω T) of an infinite disk in contact with an incompressible viscous rotating (with angular velocity aΩ) fluid of semi-infinite extent is analysed when the amplitude parameter α( = b/a) varies from zero to infinity. Composite solutions valid over the whole of the flow regime and specific expressions for the shearing stress components at the disk and for the axial flow in the far region are obtained for low and high frequencies of torsional oscillations. Using the method of matched asymptotic expansions, we find that the region of the mean flow increases with α and reaches a maximum before settling down to the Rosenblat profile. Series expressions (for α < 1) are deduced for physical quantities of interest when the fluid in the far field and the disk are rotating with different angular velocities (in the same or in the opposite sense), which agree well with the known numerical results. (Received: April 7, 2003; revised: September 29, 2005)  相似文献   

18.
In Ref. 1, the author claimed that the problem y=y 3 is soluble only for a certain range of the parameter . An analytic approach, as adopted in the following contribution, reveals that a unique solution exists for any positive value of . The solution is given in closed form by means of Jacobian elliptic functions, which can be numerically computed very efficiently. In the limit 0+, the solutions exhibit boundary-layer behavior at both endpoints. An easily interpretable approximate solution for small is obtained using a three-variable approach.  相似文献   

19.
We derive relationships between the shape deformation of an impenetrable obstacle and boundary measurements of scattering fields on the perturbed shape itself. Our derivation is rigorous by using a systematic way, based on layer potential techniques and the field expansion (FE) method (formal derivation). We extend these techniques to derive asymptotic expansions of the Dirichlet-to-Neumann (DNO) and Neumann-to-Dirichlet (NDO) operators in terms of the small perturbations of the obstacle as well as relationships between the shape deformation of an obstacle and boundary measurements of DNO or NDO on the perturbed shape itself. All relationships lead us to very effective algorithms for determining lower order Fourier coefficients of the shape perturbation of the obstacle.  相似文献   

20.
In view of singularly perturbed problems with complex inner layer phenomenon,including contrast structures(step-step solution and spike-type solution),corner layer behavior and right-hand side discontinuity,we carry out the process with sewing connection.The presented method of sewing connection for singularly perturbed equations is based on the two points singularly perturbed simple boundary problems.By means of sewing orbit smoothness,we get the uniformly valid solution in the whole interval.It is easy to prove the existence of solutions and deal with the high dimensional singularly perturbed problems.  相似文献   

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