拟线性蜕化抛物型方程广义解的正则性和唯一性

<正> 考虑拟线性蜕化抛物型方程的混合问题: u_t=(u~m)xx+b(u)u_x,Q:{00},(1) u(0,t)=ψ_1(t),t≥0,(2) u(1,t)=ψ_2(t),t≥0,(3) u(x,0)=u_o(x),0≤x≤1,(4) 其中m>1,u_o(x),ψ_i(t)(i=1,2)适合条件:     

两相不定常连续铸钢问题有限元逼近的收敛性分析

记Ω=(0,1)×(0.τ)为钢锭区域,Ω_τ=(0,T)×Ω,Ω_τ=Ω_1(t)∪Ω_2(t),t∈(0,T),其中Ω_1(t)与Ω_2(t)分别表示液态与固态区域。时刻t时的自由界面由F(t)={(x,z)∈Ω,s(X,Z,t)=0}表示,F=(?)F(t)。 设u=u(X,Z,t)表示温度。作变换后不妨设Ω,(t)上     

EXISTENCE OF PERIODIC SOLUTIONS OF SYSTEM OF DIFFERENCE EQUATIONS

This paper studies the nonautonomous nonlinear system of difference equationsΔx(n)=A(n)x(n)+f(n,x(n)),n∈Z,(*) where x(n)∈R~N,A(n)=(a_(ij)(n))N×N is an N×N matrix,with a-(ij)∈C(R,R) for i,j= 1,2,3,...,N,and f=(f_1,f_2,...,f_N)~T∈C(R×R~N,R~N),satisfying A(t+ω)=A(t),f(t+ω,z)=f(t,z) for any t∈R,(t,z)∈R×R~N andωis a positive integer.Sufficient conditions for the existence ofω-periodic solutions to equations (*) are obtained.     

解轴对称Laplace方程的间接边界积分方程的机械求积法与分裂外推算法

1引 言函数u∈C2(V)∩ C(V)称为内(外)问题的解,如果u分别满足下面Laplace方程的Dirichlet问题{△u(x)=0,x∈vUVc u(x)=h(x),x∈S这里,x=(x1,x2,x3),V CR3由二维有界连通区域Ω绕z轴旋转而成,S=(O)V是它的边界由分段光滑的曲线Г绕z轴旋转而成,n是V的外单位法向,(V)=VUS,Vc=R3＼(V).对于外问题要求u在无穷远处满足正则性条件,即当｜x｜→∞时,u(x)=O(1/(｜x｜),▽(u(x))=O(1/｜x｜2·根据单层位势理论[3],(1.1)可以转化为第一类的边界积分方程h(x0)=∫s(u)*(x;x0)ρ(x)dS,(ν)x0∈S,这里,ρ(x)是边界S上连续分布的密度函数,(u)*(x;x0)=1/4π｜x- x0｜是三维Laplace方程的基本解,｜x-x0｜表示x和x0之间的距离.     

二阶非线性微分方程在无穷区间上的边值问题

其中f(t),h_i(x)为连续函数,并且f(t)≠0,h_i(x)>0(x≠0,i=1,2)。在条件(C)之下的方程(X)仍属较一般的类型。例如:设h_1(x)=h_2(x)=h(x),则有方程x=f~2(t)xh(x);再设h(x)=|x|~n(n>0),便得广义Emden-Fowler方程(见文献[1],第7章):x=f~2(t)x|x|~n。     

一类非线性Schr dinger方程的高精度守恒数值格式

1引言本文讨论下面非线性Schr(?)dinger方程(NLS)方程的初边值问题:i(?)u/(?)t (?)~2u/(?)x~2 2|u~2|u=0,(1) u(x_l,t)=u(x_r,t)=0,t>0,(2) u(x,0)=u_0(x),x_l≤x≤x_r,(3)其中u(x,t)是复值函数,u_0(x)为已知的复值函数,i~2=-1.该问题有着如下的电荷与能量守恒关系:     

含爆轰波的间断解的渐近性

<正> 在[1]中我们研究了如下的初值问题:/t(u+qz)+/zf(u)=υ ~2u/x~2,(1)z/t=-kφ(u)z,(2)u(x,0)=u_0(x),z(x,0)=z_0(x)(3)当υ=+0,K=+∞时的弱解.其中常数q>0,υ,K,q分别代表了粘性系数、化学反应速率和束缚能,u是一个综合变量,它代表了密度、速度和温度,z是未燃气体的     

非线性双曲型方程的混合元方法

1　引　　言考虑下述非线性双曲型方程的混合问题:c(x,u)utt-.(a(x,u)u)=f(x,u,t),　　x∈Ω,t∈J,(1.1)u(x,0)=u0(x),　　x∈Ω,(1.2)ut(x,0)=u1(x),　　x∈Ω,(1.3)u(x,t)=-g(x,t),　　(x,t)∈Ω×J,(1.4)其中ΩR2是一具有Lipschitz边界Ω的有界区域,J=[0,T],0相似文献   

介绍一个函数方程

定义二元函数f(x,y)=xy 1,容易验证它满足性质: (1)f(x,0)=1; (2)f(f(x,y),z)=f(z,xy) z. 事实上,f(f(x,y),z)=f(x,y)·z 1=(xy 1)z 1=(z·xy 1) z=f(z,xy) z.     

一类带弱奇异核非线性偏积分微分方程的全离散有限元

1引言我们将研究下面一类带弱奇异核非线性偏积分微分方程的数值解:u_t-▽·(a(u)▽u)-integral from n=0 to tβ(t-s)△u(s)ds=f(u),x∈Ω,t∈(?),(1.1) u(·,t)=0,x∈(?)Ω,t∈J,(1.2) u(·,0)=v(x),x∈Ω,(1.3)其中Ω为平面上的凸角域,J=(0,T],α和f为R上的光滑函数,满足0相似文献   

Multisymplectic Fourier pseudo-spectral integrators for Klein-Gordon-Schrödinger equations

A multisymplectic Fourier pseudo-spectral scheme,which exactly preserves the discrete multisymplectic conservation law,is presented to solve the Klein-Gordon-Schrdinger equations.The scheme is of spectral accuracy in space and of second order in time.The scheme preserves the discrete multisymplectic conservation law and the charge conservation law.Moreover,the residuals of some other conservation laws are derived for the geometric numerical integrator.Extensive numerical simulations illustrate the numerical behavior of the multisymplectic scheme,and demonstrate the correctness of the theoretical analysis.     

一个解KdV方程的满足两个守恒律的差分格式

Korteweg-de Vries(KdV)方程是人们在研究一些物理问题时得到的非线性波 动方程,其解满足无穷多个守恒律．本文为该方程设计了一种差分格式,其采用的是有限 体积法．但与传统的有限体积法不同的是,它的数值解同时满足两个相关的守恒律．这样 可以更好地保持解的物理上的守恒性质．数值例子表明这一算法是有效的．     

膜自由振动的多辛方法

基于Hamilton空间体系的多辛理论研究了膜自由振动问题,讨论了构造复合离散多辛格式的方法,并构造了一种典型的9×3点半隐式的多辛复合离散格式,该格式满足多辛守恒律、能量守恒律和动量守恒律．数值算例结果表明该多辛离散格式具有较好的长时间数值稳定性．     

ON THE CENTRAL RELAXING SCHEMES I:SINGLE CONSERVATION LAWS

1. IntroductionIn [6], Jin and adn constructed a class of uPWind relaxing schemes for nonlinearconservation lawswith initial data u(0, x) ~ "o(x), x ~ (xl, ...t -cd), by using the idea of the local relaxation approximation [2,3,6,10].The relaxing scheme is obtained in the following way: A linear hyperbolic systemwith a stiff source term is first constructed to approximate the original equation (1.1)with a small dissipative correction. Then this linear hyperbolic system is solved easilyby und…     

A Splitting Method for a CABARET Scheme Approximating a Nonuniform Scalar Conservation Law

In this paper, a splitting method for a CABARET scheme approximating a nonuniform scalar conservation law with a convex and monotonically increasing flux function is proposed. It is shown that at the first step of this method, when a uniform conservation law is approximated, the CABARET scheme is monotone and its numerical solutions do not have nonphysical oscillations in shock wavefronts. Test computations illustrating these properties of the modified CABARET scheme are presented.     

Monotonization of flux, entropy and numerical schemes for conservation laws

Using the concept of monotonization, families of two step and k-step finite volume schemes for scalar hyperbolic conservation laws are constructed and analyzed. These families contain the FORCE scheme and give an alternative to the MUSTA scheme. These schemes can be extended to systems of conservation law.     

一维双曲守恒方程组的Taylor-Galerkin有限元方法

１．引言 在文章［８］中,利用双曲守恒律的Ｈａｍｉｌｔｏｎ－Ｊａｃｏｂｉ方程形式,应用 Ｇａｌｅｒｋｉｎ有限元给出了求解一维双曲守恒律的计算方法．不同于间断有限元方法［２］、［３］和 Ｔａｙｌｏｒ－Ｇａｌｅｒｋｉｎ有限元方法［１］求解双曲守恒律,文章［８］采用连续 Ｇａｌｅｒｋｉｎ有限元求解双曲守恒律． 在文章［８］中,对差分方法和有限元方法求解双曲守恒律作了较为详细的讨论．同时在文章［８］中,采用积分变换,将双曲守恒律方程变成 Ｈａｍｉｌｔｏｎ－Ｊａｃｏｂｉ方程形式．由于 Ｈａｍｉｌｔｏｎ－Ｊａｃｏ…     

守恒格式稳定性分析与耗散守恒格式

本文从守恒格式出发,建立分析稳定性和耗散性的启发性方法和Fourier分析方法,给出了耗散守恒格式的严格定义及三点耗散守恒格式的充要条件。应用本文的方法,重新分析了三点格式,得到如下结论:某些常系数耗散格式,在某些情况下,之所以会得到非物理解或发生非线性不稳定,是由于该格式在这些情况下,已经是零耗散的或是负耗散     

二维双曲守恒律的大时间步长Godunov方法(英文)

考虑了关于二维守恒律的大时间步长Godunov方法.该方法是关于一维问题的自然推广.证明了文中给出的数值流函数下,该方法是守恒的.进一步还给出了近似Riemann解应满足的条件,并且证明了利用满足这些条件的近似Riemann解的大时间步长Godunov方法守恒.最后,补充证明了满足这些条件的近似Riemann解是满足熵条件的.     

Implicit kinetic schemes for scalar conservation laws

Based on kinetic formulation for scalar conservation laws, we present implicit kinetic schemes. For time stepping these schemes require resolution of linear systems of algebraic equations. The scheme is conservative at steady states. We prove that if time marching procedure converges to some steady state solution, then the implicit kinetic scheme converges to some entropy steady state solution. We give sufficient condition of the convergence of time marching procedure. For scalar conservation laws with a stiff source term we construct a stiff numerical scheme with discontinuous artificial viscosity coefficients that ensure the scheme to be equilibrium conserving. We couple the developed implicit approach with the stiff space discretization, thus providing improved stability and equilibrium conservation property in the resulting scheme. Numerical results demonstrate high computational capabilities (stability for large CFL numbers, fast convergence, accuracy) of the developed implicit approach. © 2002 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 18: 26–43, 2002