BBM-Burgers方程解得衰减估计

本文研究了一维空间的BBM-Burgers方程.利用时频分解和能量估计等工具,在解整体存在的前提下,得到了本方程柯西问题解的某些衰减估计.     

不连续一阶微分系统广义解的存在唯一性定理和迭代逼近

本文利用混合单调技巧,得到了不连续一阶微分系统初值问题广义解的存在唯一性定理;构造了一致收敛于广义解的迭代序列,且得到了收敛速度的估计式。本文考虑R~n中不连续一阶常微分方程初值问题。     

非Fourier温度场分布的奇摄动解

应用非Fourier热传导定律构建了单层材料中温度场模型，即一类在无界域上带小参数的奇摄动双曲方程，通过奇摄动展开方法，得到了该问题的渐近解.首先应用奇摄动方法得到了该问题的外解和边界层矫正项，通过对内解和外解的最大模估计和关于时间导数的最大模估计以及线性抛物方程理论，得到了内外解的存在唯一性，从而得到了解的形式渐近展开式.通过余项估计，给出了渐近解的L2估计，得到了渐近解的一致有效性，从而得到了无界域上温度场的分布.通过奇摄动分析，给出了非Fourier 温度场与Fourier 温度场的关系，描述了非Fourier温度场的具体形态.     

一类糖酵解模型正平衡解的存在性分析

研究生化反应中具有代表性的一类糖酵解模型.运用先验估计讨论非常数正平衡解的不存在性,得到非常数正平衡解存在的必要条件.在常数平衡解Turing不稳定的基础上,利用度理论方法和解的先验估计,进一步给出非常数正平衡解存在的充分条件.     

两种块校正最小二乘问题的代数关系

1 引言 在求解工程问题中,我们常常应用最小二乘方法 min‖Ax-b‖_2,A∈R~(m×n),m≥n (1.1) x∈R~n去得到问题的数值近似解或估计系统的未知参数.我们常常已知(1)的解,而希望求解修改问题     

一类具有Neumann边界条件的曲率方程解的估计

研究了一类具有Neumann边界条件的抛物方程解的性质,通过微分方法得到了一类边值问题解的估计,并得到了拟线性方程解的存在性.     

半空间上具耦合非线性边界扩散系统的爆破性质

考虑半空间上具耦合非线性边界条件的热方程组解的爆破估计. 给出了爆破速率的上界和下界估计, 得到了具零初值解的惟一性和非惟一性结果.     

紧黎曼流形上的椭圆边界值问题

讨论一类非齐次非线性椭圆边界值问题.利用极大值原理证明了该问题解的梯度估计.作为它的应用得到了解的效率比估计.     

一类奇摄动半线性时滞抛物型偏微分方程的渐近解

文中讨论了一类奇摄动时滞抛物型偏微分方程的初边值问题,得到了其形式渐近展开,证明了奇摄动半线性时滞偏微分方程的极大值原理,从而得到了最大值估计及相应的Schuader估计.在此基础上,得到了柱状区域上解的存在唯一性和渐近解的一致有效性.     

细菌模型的非协调有限元分析

将非协调元应用于描述细菌传播的反应扩散方程组的初边值问题.借助单元的一些特性和非协调误差估计技巧,分别在半离散和全离散有限元格式下,研究了其数值解与精确解的误差估计,得到了最优的误差估计以及超逼近结果.     

类渐近线性p&q-Laplace方程弱解的全局衰减性

该文研究椭圆型方程 {Δ_pu+m|u|^p-2u-Δ_qu+n|u|^q-2u=g(x, u), x∈R^N, u∈ W^{1, p}(R^N)∩W^{1, q}(R^N) 弱解在全空间R^N上的衰减性, 其中m, n ≥ 0, N≥3, 1 < q < p < N, g(x, u)关于u满足类渐近线性. 证明了该方程的 弱解在无穷远处关于|x|呈指数衰减性.     

广义逆多项式模的Attached素理想

设R是有单位元1的结合环,(S,≤)是严格全序Artin幺半群,M_R是右R-模,Att(M_R)与Att([M~(S,≤)]_([[R~(S,≤)]]))分别表示模M_R与广义逆多项式模[M~(S,≤)]_([[R~(S,≤)]])的所有Attached素理想组成的集合.该文主要讨论了广义幂级数环[[R~(S;≤)]]广义逆多项式模[[R~(S;≤)]]的Attached素理想的相关性质,证明了在一定条件下,有Att([M~(S,≤)]_([[R~(S,≤)]])={[[PR~(S;≤)]]P∈Att(M_R)}.这一结论表明广义逆多项式模([M~(S,≤)]_([[R~(S,≤)]])的Attached素理想在一定条件下可以用模M_R的Attached素理想来刻画,推广了Annin S在文献[1]中关于斜多项式环上逆多项式模的Attached素理想的相关结论.     

Nonexistence of Positive Solutions of PDE's with p-Laplacian

We derive conditions on the function c : Rⁿ → R which guarantee that the PDE with p-Laplacian div (❘∇ u❘^p-2∇ u ) + c(x)❘u❘^p-2u =0, p >1, has no positive solution either in Rⁿ or in the domain Omega_r :={x ∈ Rⁿ : ❘x❘ ≧r} with r arbitrarily large. This revised version was published online in June 2006 with corrections to the Cover Date.     

Existence and decay of solutions in full space to Navier-Stokes equations with delays

We consider the Navier-Stokes equations with delays in Rⁿ,2≤n≤4. We prove existence of weak solutions when the external forces contain some hereditary characteristics and uniqueness when n=2. Moreover, if the external forces satisfy a time decay condition we show that the solution decays at an algebraic rate.     

A new continuation method for complementarity problems with uniformP-functions

The complementarity problem with a nonlinear continuous mappingf from the nonnegative orthantR ₊ ⁿ ofR ⁿ intoR ⁿ can be written as the system of equationsF(x, y) = 0 and(x, y) R ₊ ²ⁿ , whereF denotes the mapping from the nonnegative orthantR ₊ ²ⁿ ofR ²ⁿ intoR ₊ ⁿ × Rⁿ defined byF(x, y) = (x ₁y₁,,x_ny_n, f₁(x) – y₁,, f_n(x) – y_n) for every(x, y) R ₊ ²ⁿ . Under the assumption thatf is a uniformP-function, this paper establishes that the mappingF is a homeomorphism ofR ₊ ²ⁿ ontoR ₊ ⁿ × Rⁿ. This result provides a theoretical basis for a new continuation method of tracing the solution curve of the one parameter family of systems of equationsF(x, y) = tF(x ⁰, y⁰) and(x, y) R ₊ ²ⁿ from an arbitrary initial point(x ⁰, y⁰) R ₊ ²ⁿ witht = 1 until the parametert attains 0. This approach is an extension of the one used in the polynomially bounded algorithm recently given by Kojima, Mizuno and Yoshise for solving linear complementarity problems with positive semi-definite matrices.     

Homogenization of the parabolic cauchy problem in the Sobolev class H<Superscript>1</Superscript>(R<Superscript>d</Superscript>)

Homogenization in the small period limit for the solution ue of the Cauchy problem for a parabolic equation in R^d is studied. The coefficients are assumed to be periodic in R^d with respect to the lattice ɛG. As ɛ → 0, the solution u ɛ converges in L2(R^d) to the solution u0 of the effective problem with constant coefficients. The solution u ɛis approximated in the norm of the Sobolev space H ¹(R^d) with error O( ɛ); this approximation is uniform with respect to the L2-norm of the initial data and contains a corrector term of order ɛ. The dependence of the constant in the error estimate on time t is given. Also, an approximation in H ¹(R^d) for the solution of the Cauchy problem for a nonhomogeneous parabolic equation is obtained.     

A symmetry result for the p-laplacian equation via the moving planes method

Thsi paper is concerned with a positive solution u of the non–homogeneous p–Laplacian equation in an open, bounded, connected subset Ω of Rⁿ with C² boundary. We assume that u verifies overdetermined boundary conditions and we prove that of us has only one critial point Ω thenΩ is a ball and u is radially symmetric; to prove this result we use the moving planes method introduced by J.Serrien. Using the same technique we also prove that the result is stable in the following sense: the boundary of Ω tends to the boundary of a sphere as the diameter of the critical set u tends to 0.     

含有共振项的p-Laplace方程解的存在性

主要讨论一类非线性项在无穷远处渐近|u|~(p-2)u增长的p-Laplace方程的Dirichlet边值问题,利用环绕定理证明了当λ_1≤λ(λ_1为算子(-△_p,W_1,p~0(Ω))第一特征值)时,方程存在非平凡解.     

Deciding consistency of systems of exponential-polynomial inequalities in subexponential time

Let the polynomials P₁...,P_k Z[u,X₁...,X_n], h Z[X₁,...,X_n] have degrees, and assume that absolute values of any coefficients of P_i and h is less than or equal to 2^M for all l i k. The article present an algorithm to recognize the consistency in Rⁿ of the system of inequalities, in time polynomial in . This result is a generalization of the subexponential-time algorithms of [4, 5, 23] for deciding consistency of systems of polynomial inequalities, and can be considered a contribution to the solution of Tarski's decidability problem concerning the first order theory of reals with exponentiation [1].Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akademii Nauk SSSR, Vol. 176, pp. 3–52, 1989.     

Saddle solutions of nonlinear elliptic equations involving the p-Laplacian

We prove the existence of saddle solutions of nonlinear elliptic equation involving the p-Laplacian