DECAY OF POSITIVE WAVES OF HYPERBOLIC BALANCE LAWS

Historically,decay rates have been used to provide quantitative and qualitative information on the solutions to hyperbolic conservation laws.Quantitative results include the establishment of convergenc...     

ASYMPTOTIC STABILITY OF RAREFACTION WAVE FOR GENERALIZED BURGERS EQUATION

This paper is concerned with the stability of the rarefaction wave for the Burgers equationwhere 0 ≤ a < 1/4p (q is determined by (2.2)). Roughly speaking, under the assumption that u_ < u , the authors prove the existence of the global smooth solution to the Cauchy problem (I), also find the solution u(x, t) to the Cauchy problem (I) satisfying sup |u(x, t) -uR(x/t)| → 0 as t → ∞, where uR(x/t) is the rarefaction wave of the non-viscous Burgersequation ut f(u)x = 0 with Riemann initial data u(x, 0) =     

求解带刚性源项标量双曲型守恒律方程的保有界WCNS格式

带刚性源项的双曲守恒律方程是很多物理问题,特别是化学反应流的数学模型.本文考虑带刚性源项的标量双曲型守恒律方程,通过时空分离的方式,发展了一类保有界的WCNS格式.对于空间离散,我们将参数化的通量限制器推广到WCNS框架,使得方程对流项离散后满足极值原理.对于时间离散,我们将半离散的WCNS改写成指数形式,采用三阶修正...     

NONLINEAR STABILITY OF RAREFACTION WAVES FOR A RATE-TYPE VISCOELASTIC SYSTEM

51.IntroductionInthispaper,westudythefollowingrate-typeviscoelasticsystem,i.e.,wherevand(--p)denotestrainandstress,uisrelatedtotheparticlevelocity,EisapositiveconstantcalledthedynamicYOung'smodulus,T>0isarelaxationtime.Thissystemwasproposedinfi6]tointroducearelaxationapproximationtothefollowingsystemSincethesystem(1.2)canbeobtainedfrom(1.1)byanexpansionprocedureasthefirstorder,itisnaturaltoexpectthatthesolutionof(1.1)convergestothatof(1.2)asT-0.However,thezerolimitconvergencehasnotbeenestabl…     

ASYMPTOTIC DECAY TOWARD RAREFACTION WAVE FOR A HYPERBOLIC-ELLIPTIC COUPLED SYSTEM ON HALF SPACE

We consider the asymptotic behavior of solutions to a model of hyperbolicelliptic coupled system on the half-line R＋ = （0, ∞）,with the Dirichlet boundary condition u（0, t） = 0. S. Kawashima and Y. Tanaka [Kyushu J. Math., 58（2004）, 211-250] have shown that the solution to the corresponding Cauchy problem behaviors like rarefaction waves and obtained its convergence rate when u_ u＋. Our main concern in this paper is the boundary effect. In the case of null-Dirichlet boundary condition on u, asymptotic behavior of the solution （u, q） is proved to be rarefaction wave as t tends to infinity. Its convergence rate is also obtained by the standard L2-energy method and Ll-estimate. It decays much lower than that of the corresponding Cauchy problem.     

一个刚性守恒律方程组的全隐式差分方法

１．引言本文研究如下非线性刚性守恒律方程组的全隐式差分逼近． 方程（1．１）中的源项ｇ（ｕ,ｖ）定义为 ｇ（ｕ,ｖ）＝ｖ－（１－μ）ｆ（ｕ）,（１．２）其中ｆ是ｕ的一个给定函数,δ是一个小正参数,称为松弛时间,μ是参数．方程组（１．１）频繁出现于粘弹性力学中． 在零松弛时间限（δ→０）下,从（１．１）可得到如下方程组该方程组通常称为“平衡”模型,而方程组（１．１）称为“非平衡”模型． 文中将假设μ满足 ０＜ μ＜ １,（１．４）以便保证拟稳定性条件［１９,２０］和次特征条件［１１,２,３］： λ１≤λ＊…     

具有小周期孔洞弹性结构的双尺度渐近分析

本文对具有小周期孔洞的复合材料弹性结构进行研究,得到了位移函数一类可计算的双尺度渐近展开式,并给予严格的理论证明．     

一个燃烧波模型解的存在唯一性与渐近行为

本文讨论一类燃烧波模型.在较弱的条件下证明该问题解的存在唯一性,并给出了解的渐近行为.     

超经典Boussinesq系统的守恒律和自相容源

本文研究了超经典Boussinesq系统.利用已有的超经典Boussinesq方程族及其超哈密顿结构,构造了带自相容源的超经典Boussinesq方程族,并通过引入变量F和G,获得了超经典Boussinesq方程族的守恒律.     

MULTISCALE ASYMPTOTIC EXPANSION FOR A CLASS OF HYPERBOLIC-PARABOLIC TYPE EQUATION WITH HIGHLY OSCILLATORY COEFFICIENTS

In this paper, we will discuss the asymptotic behaviour for a class of hyperbolic -parabolic type equation with highly oscillatory coefficients arising from the strong-transient heat and mass transfer problems of composite media. A complete multiscale asymptotic expansion and its rigorous verification will be reported.     

变系数情形下Criss-Cross三角形线性元的渐近展式与超收敛

本文讨论了二阶椭圆方程变系数情形下Criss-Cross三角形线性元的超收敛性质,得到了有限元的渐进展式、外推及高精度组合公式等结果.     

双曲型守恒律方程组的Godunov格式中离散激波的渐近稳定性

１引言我们研究求解守恒律初值问题的Ｇｏｄｕｎｏｖ格式,其中ｆ：ＲＮ→ＲＮ,并且方程（１）是严格双曲型的．我们还假定　的特征值（）,…,Ｎ（）均为非零,并且每一个特征在Ｌａｘ意义下或者是真正非线性的,或者是线性退化的．利用Ｍａｊｄａ和Ｒａｌｓｔｏｎ的一个结果［６］,我们将证明离散行波激波的存在性,然后证明激波的渐近稳定性,也即,如果初值是激波的一个小的摄动,则当ｔ→由Ｇｏｄｕｎｏｖ格式得到的解趋于一个平移了的行波激波．在［１０］中我们证明了对于Ｌａｘ－Ｆｒｉｅｄｒｉｃｈｓ格式的渐近稳定性,所用的加…     

改进的椭圆型问题一阶渐近展开误差估计

1引言考虑下述多尺度椭圆问题:■(1)其中椭圆算子A_ε定义为A_ε=-■/(■x_i)(a_(ij)~ε■/(■x_j).(2)本文使用爱因斯坦求和约定,重复指标表示求和.系数a_(ij)~ε(x)=a_(ij)(x/ε)满足下列条件:     

小展弦比波的Green-Naghdi渐进模型的行波解

本文研究了小展弦比波的Green-Naghdi渐进模型. 利用平面自治系统的稳定性分析方法, 在不同的参数条件下, 讨论了它的行波系统的分岔并且给出了对应的相图, 得到了光滑周期波解, 广义扭波解, 广义反扭波解, 广义紧波解, 周期尖波解, 孤波解和孤立尖波解的精确表达式. 进一步, 通过数学软件Maple模拟了这些解.     

含时滞的线性偏泛函微分方程解的渐近行为

本文对一类含有时滞的抛物偏泛函微分方程解的渐近行为进行了讨论。分别就两种不同的边界条件，采用Ｌｉａｐｕｎｏｖ泛函及Ｌ—ｐ—估计，获得了其解全局稳定、振动的若干简洁充分条件     

DECAY RATES OF PLANAR VISCOUS RAREFACTION WAVE FOR MULTI-DIMENSIONAL SCALAR CONSERVATION LAW WITH DEGENERATE VISCOSITY ON HALF SPACE

We investigate the decay rates of the planar viscous rarefaction wave of the initial-boundary value problem to scalar conservation law with degenerate viscosity in several dimensions on the half-line space, where the corresponding one-dimensional problem admits the rarefaction wave as an asymptotic state. The analysis is based on the standard L2-energy method and L1-estimate.     

一种求解跳系数椭圆标量方程的渐近展开方法的误差分析

本文研究了具有跳系数(或多尺度性质)的椭圆型PDEs问题.利用渐近展开方法,将具有多尺度性质的PDEs模型问题解耦为若干光滑系数(或单尺度性)的PDEs问题进行求解,获得了和经典线性有限元方法在.0意义下同样的误差阶,表明了该方法的有效性.     

Asymptotic behavior of solutions to anisotropic conservation laws in two-dimensional space

In this paper, we investigate the asymptotic behavior of solutions for anisotropic conservation laws in two-dimensional space, provided with step-like initial conditions that approach the constant states u_± (u₋<u₊) as x→±∞, respectively. It shows that there is a global classical solution that converges toward the rarefaction wave, ie, the unique entropy solution of the Riemann problem for the nonviscous Burgers' equation in one-dimensional space.     

DECAY OF POSITIVE WAVES OF HYPERBOLIC BALANCE LAWS Dedicated to Professor Constantine M. Dafermos on the occasion of his 70th birthday

Historically,decay rates have been used to provide quantitative and qualitative information on the solutions to hyperbolic conservation laws.Quantitative results include the establishment of convergence rates for approximating procedures and numerical schemes.Qualitative results include the establishment of results on uniqueness and regularity as well as the ability to visualize the waves and their evolution in time.This work presents two decay estimates on the positive waves for systems of hyperbolic and genuinely nonlinear balance laws satisfying a dissipative mechanism.The result is obtained by employing the continuity of Glimm-type functionals and the method of generalized characteristics [7,17,24].     

一维粘性守恒律初边值问题粘性激波解的渐近稳定性

本文考虑一维可压缩Navier-Stokes方程有关初边值问题粘性激波解的渐近稳定性,通过L~2-能量估计,证明了在小扰动情况下,粘性激波是稳定的。