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SINGULAR SOLUTIONS FOR A CONVECTION DIFFUSION EQUATION WITH ABSORPTION

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Acta math.matica Scientia 1995年第4期15卷 431-441页

作者：赵俊宁 dept. of math. Jilin University Changchun 130023 China

In this paper we discuss the existence and nonexistence of singular solutions for a porous medium equations with convection and absorption terms.

关键词： convection diffusion equation singular solution existence and nonexistence

REGULARITY OF H^1 ∩L^(n((γ-1)/(2-γ))) WEAK SOLUTIONS FOR NONLINEAR ELLIPTIC SYSTEMS

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Acta math.matica Scientia 1990年第2期10卷 173-184页

作者：何旭东陈宝耀 dept. of math. Zhongshan Univ. Guangzhou China

Let us consider the following elliptic systems of second order-D_α(A_i~α(x, u, Du))=B_4(x, u, Du), i=1, …, N, x∈Q(?)R^n, n≥3 (1) and supposeⅰ) |A_i~α(x, u, Du)|≤L(1+|Du|);ⅱ) (1+|p|)^(-1)A_i~α(x, u, p)are H(?)lder-continuous functions with some exponent δ on (?)×R^N uniformly with respect to p, i.e.ⅲ) A_i~α(x, u, p) are differentiable function in p with bounded and continuous derivativesⅳ)ⅴ) for all u∈H_(loc)~1(Ω, R^N)∩L^(n(γ-1)/(2-γ))(Ω, R^N), B(x, u, Du)is ineasurable and |B(x, u, p)|≤a(|p|~γ+|u|~τ)+b(x), where 1+2/n0, b(x)∈L2n/(n+2), n^2/(n+2)+e(Ω), (?)ε>***. Only bounded open set Q will be considered in this paper; for all p≥1, λ≥0, which is clled a Morrey *** assumptions ⅰ)-ⅳ) hold, Giaquinta and Modica have proved the regularity of both the H^1 weak solutions of (1) under controllable growth condition |B|≤α(|p|~γ+|u|^((n+2)/(n-2))+b, 0<γ≤1+2/n and the H^1∩L~∞ weak solutions of (1) under natural growth condition |B|≤α|p|~2+b with a smallness condition 2aM<λ(|u|≤M), which implys that the H^1∩L~∞ weak solutions have the same regularty in the case of 1+2/n<γ<2. In the case of γ=2, many counterexamples (see [2] showed that u must be in H^1L~∞, while in the case of 1+2/n<γ<2, we consider the H^1∩L^n(γ-1)/(2-γ) weak solutions of (1), weaken the instability conditions upon them (from L~∞ to L^n(γ-1)/(2-γ) and obtain the same regularity results. Finally we show that the exponent n(γ-1)/(2-γ) can not be docreased anymore for the sake of the regularity *** 1. We call u∈H^1∩L^n(γ-1)/(2-γ)(Q, R^N) be a weak solution of (1), providod that where We use the convention that repeated indices are summed. i, j go from 1 to N ann α, β from 1 to n.

关键词： WEAK SOLUTIONS FOR NONLINEAR ELLIPTIC SYSTEMS REGULARITY OF H~1

APPROXIMATION OF SINGULAR INTEGRALS BY INTERPOLATING SPLINES

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Acta math.matica Scientia 1991年第1期11卷 20-31页

作者：王建忠 dept. of math. Wuhan Univ. Wuhan China

In this paper we are mainly concerned with the approximation of the following type of singular Integrals: where w(t)≥0 is a weight function, f(x) a real continuous function on [a, b], satisfying certain smooth condit... 详细信息

关键词： In APPROXIMATION OF SINGULAR INTEGRALS BY INTERPOLATING SPLINES

SOME PROBLEMS FOR LINEAR ELASTIC SYSTEMS WITH DAMPING

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Acta math.matica Scientia 1990年第3期10卷 319-326页

作者：黄发伦 dept. of math. Sichuan Univ. Chengdu China

In the present paper we investigate linear elastic systems with damping in Hilbert spaces, where A and B ars unbounded positive definite linear operators. We have obtained the most fundamental results for the holomorphic property and exponential stability of the semigroups associated with these systems via inclusion relation of the domains of A and B.

关键词： Th SOME PROBLEMS FOR LINEAR ELASTIC SYSTEMS WITH DAMPING IA BA

THE CAUCHY TYPE INTEGRAL FOR M-ANALYTIC FUNCTION AND ITS APPLICATION

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Acta math.matica Scientia 1990年第2期10卷 149-166页

作者：林伟戴道清 dept. of math. Zhongshan Univ. Guangzhou China

In this paper, the Cauchy type integral for M-analytic function is investigated which is by definition the regular solution of the elliptic system f_x+Mf_y=0, where M is a constant m×m matrix without any real eigenva... 详细信息

关键词： Pr THE CAUCHY TYPE INTEGRAL FOR M-ANALYTIC FUNCTION AND ITS APPLICATION

ON MULTIPARAMETER CHACONORNSTEIN THEOREM

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Acta math.matica Scientia 1991年第2期11卷 225-229页

作者：钱能生 dept. of math. Wuhan University Wuhan China

In this paper we prove continuous multiparameter Chancon-Ornstein theorem which is described in the discrete case by Louis Sucheston.

关键词： ON MULTIPARAMETER CHACONORNSTEIN THEOREM

ON ALMOST ISOMETRIES FROM L^1 (μ) INTO L~∞(v) OR C_b (△)

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Acta math.matica Scientia 1992年第3期12卷 308-311页

作者：定光桂 dept. of math. Nankai University Tianjin 300071

Let μ,ν be measures with diem L^1(μ) =dim L~∞(ν)=∞ and ⊿ be a 'subinterval' of the real line. Let E=L~∞(ν) or C_b(⊿), in this paper it turns out that the IAP for the space B(L^1(μ)→E) has a negative answer.

关键词： IAP OR C_b INTO L ON ALMOST ISOMETRIES FROM L~1

GLOBAL SOLUTION OF NONLINEAR DEGENERATE SYSTEMS OF FILTRATION TYPE IN SEVERAL SPACE VARIABLES

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Applied math.matics(A Journal of Chinese Universities) 1999年第1期14卷 30-44页

作者： Lu Guofu dept. of math. Putian College Fujian

In this paper the following nonlinear degenerate parabolic systemsu t=Δ x( grad φ(u))+α·Δb(u)+f(x,t,u)with Dirichlet boundary conditions are discussed, where u, grad φ(u),b and f are vector valued functions and x∈Ω R N. Under some structure conditions on the terms of the systems, the results on existence and uniqueness of global solutions of the systems are established.

关键词： 1991 MR Subject Classification 35K65 35R35

LAGRANGE EQUATION OF ANOTHER CLASS OF NONHOLONOMIC SYSTEMS

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Applied math.matics and Mechanics(English Edition) 1991年第8期12卷 727-732页

作者：高普云郭仲衡 dept. of math. Xiangtan Normal School Hunan dept. of math. Peking University Beijing

Using the method of [1], the present paper derives the Lagrange equation without multipliers for another class of first-order nonholonomic dynamical systems by means of variational principle. This kind of equations is... 详细信息

关键词： nonholonomic dynamics Lagrange equation variational principle