首页 | 本学科首页   官方微博 | 高级检索  
相似文献
 共查询到20条相似文献,搜索用时 15 毫秒
1.
We consider a shallow water equation of the Camassa–Holm type, which contains nonlinear dispersive effects as well as fourth order dissipative effects. We prove that as the diffusion and dispersion parameters tend to zero, with a condition on the relative balance between these two parameters, smooth solutions of the shallow water equation converge to discontinuous weak solutions of a scalar conservation law. The proof relies on deriving suitable a priori estimates together with an application of the compensated compactness method in the L p setting.  相似文献   

2.
    
The purpose of this article is to study the asymptotic analysis of the solutions of a linear viscoelastic problem with a dissipative and source terms in a three‐dimensional thin domain Ωε. Firstly, we give the strong formulation of the problem and the existence and uniqueness theorem of the weak solution. Then, we establish some estimates independent of the parameter ε. These last will be useful to obtain the limit problem with a specific weak form of the Reynolds equation.  相似文献   

3.
张静  王彩华 《应用数学》2022,(2):355-373
本文针对含扰动参数ε的含源反应扩散方程,采用待定系数法,在三点模板的中心点处进行泰勒展开,对泰勒展式中的高阶导数项充分利用原微分方程进行"降阶",然后分别从"横向"和"纵向"两个角度进行修正,得到了两类差分格式,其中横向系列差分格式(HDS)的精度分别达到二阶、四阶和六阶.数值实验与参考格式比对效果较好,且横向差分格式...  相似文献   

4.
对于反应扩散方程解的爆破时刻研究,不仅具有理论意义,而且与安全地控制生产,控制种群密度以及环境趋化治理等实际问题密切相关.该文考虑了一类具有梯度源和非局部源的反应扩散方程解的爆破时刻下界.首先,假设区域为高维空间中的具有光滑边界的有界凸区域;其次,通过构造合适的辅助函数,利用一阶微分不等式技术和Sobolev不等式,得出解在有限时刻发生爆破时的爆破时刻下界;最后,通过两个应用实例来解释说明文中所获得的抽象结论.  相似文献   

5.
We study general zero range processes with different types of particles on a d-dimensional lattice with periodic boundary conditions. A necessary and sufficient condition on the jump rates for the existence of stationary product measures is established. For translation invariant jump rates we prove the hydrodynamic limit on the Euler scale using Yaus relative entropy method. The limit equation is a system of conservation laws, which is hyperbolic and has a globally convex entropy. We analyze this system in terms of entropy variables. In addition we obtain stationary density profiles for open boundaries.  相似文献   

6.
    
We prove that as the solutions of , , , , , , , converges in to the solution of the ODE , , where , , satisfies in for some function , , satisfying whenever for a.e. , for and for , where is a constant and is any measurable subset of .

  相似文献   


7.
    
ABSTRACT

This paper is concerned with the decay property of a nonlinear viscoelastic wave equation with linear damping, nonlinear damping and source term. Under weaker assumption on the relaxation function, we establish a general decay result, which extends the result obtained in Messaoudi [Exponential decay of solutions of a nonlinearly damped wave equation. Nodea-Nonlinear Differ Equat Appl. 2005;12:391–399].  相似文献   

8.
In this paper, we proposed a higher-order moment method in the lattice Boltzmann model for the conservation law equation. In contrast to the lattice Bhatnagar–Gross–Krook (BGK) model, the higher-order moment method has a wide flexibility to select equilibrium distribution function. This method is based on so-called a series of partial differential equations obtained by using multi-scale technique and Chapman–Enskog expansion. According to Hirt’s heuristic stability theory, the stability of the scheme can be controlled by modulating some special moments to design the third-order dispersion term and the fourth-order dissipation term. As results, the conservation law equation is recovered with higher-order truncation error. The numerical examples show the higher-order moment method can be used to raise the accuracy of the truncation error of the lattice Boltzmann scheme for the conservation law equation.  相似文献   

9.
In this work we study the conservation laws of a modified lubrication equation, which describes the dynamics of the interfacial motion in phase transition. We show that the equation is nonlinear self-adjoint and has an exact Lagrangian with an auxiliary function. As a result, by a general theorem on conservation laws proved by Nail Ibragimov recently and Noether’s theorem, some new conservation laws for the equation are obtained. Our results show that the non-locally defined conservation laws generated by Noether’s theorem are equivalent to the local ones given by Ibragimov’s theorem.  相似文献   

10.
The functional central limit theorems are proved for super-Brownian motion with immigration and their occupation time processes. For the lower dimensions, the limiting processes are Gaussian processes; For the critical dimension, the limiting processes consist of two ingredient processes of different types. Interestingly, for the higher dimensions, the limiting process for the occupation time process is of a new type.  相似文献   

11.

研究了具有空变系数源项的半线性Moore-Gibson-Thompson(MGT)方程Cauchy问题解的爆破现象。在次临界情形下,通过选择合适的能量泛函和测试函数,运用迭代方法和一些微分不等式技巧,得到了其Cauchy问题解的非全局存在性。进一步导出了其Cauchy问题解的生命跨度的上界估计。

  相似文献   

12.
雷锦志  晏平 《应用数学》2003,16(3):75-81
本文使用微分代数的技巧,研究了发展方程的守恒率与对应的行波所满足方程的首次积分之间的关系.通过文本给出的结果,我们研究了Burgers方程和Burgers—KdV方程的可积性,证明了这两类方程都只有一个守恒率.利用本文给出的方法,可以通过常微分方程的研究方法来研究某些非线性发展方程.  相似文献   

13.
    
In this paper, we consider the initial value problem for the Rosenau equation with damped term. The decay structure of the equation is of the regularity‐loss type, which causes the difficulty in high‐frequency region. Under small assumption on the initial value, we obtain the decay estimates of global solutions for n≥1. The proof also shows that the global solutions may be approximated by the solutions to the corresponding linear problem for n≥2. We prove that the global solutions may be approximated by the superposition of nonlinear diffusion wave for n = 1. Copyright © 2016 John Wiley & Sons, Ltd.  相似文献   

14.
We consider a two-fluid model of two-phase compressible flows. First, we derive several forms of the model and of the equations of state. The governing equations in all the forms contain source terms representing the exchanges of momentum and energy between the two phases. These source terms cause unstability for standard numerical schemes. Using the above forms of equations of state, we construct a stable numerical approximation for this two-fluid model. That only the source terms cause the oscillations suggests us to minimize the effects of source terms by reducing their amount. By an algebraic operator, we transform the system to a new one which contains only one source term. Then, we discretize the source term by making use of stationary solutions. We also present many numerical tests to show that while standard numerical schemes give oscillations, our scheme is stable and numerically convergent.  相似文献   

15.
This work is devoted to a class of fourth order wave equations with linear damping term and superlinear source term. After showing the uniqueness and existence of local solutions to the equations, we give necessary and sufficient conditions for global existence and finite time blow-up of these solutions. Moreover, the potential well depth is estimated.  相似文献   

16.
We study an integro-differential equation that describes the slow erosion of granular flow. The equation is a first order nonlinear conservation law where the flux function includes an integral term. We show that there exist unique traveling wave solutions that connect profiles with equilibrium slope at ±∞. Such traveling waves take very different forms from those in standard conservation laws. Furthermore, we prove that the traveling wave profiles are locally stable, i.e., solutions with monotone initial data approach the traveling waves asymptotically as t→+∞t+.  相似文献   

17.
    
We consider the magnetic induction equation for the evolution of a magnetic field in a plasma where the velocity is given. The aim is to design a numerical scheme which also handles the divergence constraint in a suitable manner. We design and analyze an upwind scheme based on the symmetrized version of the equations in the non-conservative form. The scheme is shown to converge to a weak solution of the equations. Furthermore, the discrete divergence produced by the scheme is shown to be bounded. We report several numerical experiments that show that the stable upwind scheme of this paper is robust.https://doi.org/10.1051/m2an/2009006  相似文献   

18.
We consider a non-local regularization of nonlinear hyperbolic conservation laws in several space variables. The regularization is motivated by the theory of phase dynamics and is based on a convolution operator. We formulate the initial value problem and begin by deriving a priori estimates which are independent of the regularization parameter. Following Hwang and Tzavaras we establish a kinetic decomposition associated with the problem under consideration, and we conclude that the sequence of solutions generated by the non-local model converges to a weak solution of the corresponding hyperbolic problem. Depending on the scaling introduced in the non-local dispersive term, this weak limit is either a classical Kruzkov solution satisfying all entropy inequalities or, more interestingly, a nonclassical entropy solution in the sense defined by LeFloch, that is, a weak solution satisfying a single entropy inequality and containing undercompressive shock waves possibly selected by a kinetic relation. Finally, we illustrate our analytical conclusions with numerical experiments in one spatial variable.  相似文献   

19.
This paper derives a conservation law for mean waiting times in a single-server multi-class service queueing system (M X/G/1 type queue) with setup times which may be dependent on multiple customer classes and its arrival batch size by using the work decomposition property in the queueing system with vacations.  相似文献   

20.
A symmetry analysis is performed on a (2+1)-dimensional linear diffusion equation with a nonlinear source term involving the dependent variable and its spatial derivatives. In the first part of the paper, we use the classical method to classify source terms where the original equation admits a nontrivial symmetry. In the second part of the paper, we use the nonclassical method and show that we simply recover the classical symmetries.  相似文献   

设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号