摘要：
The optimal control problem governed by a state equation is addressed. Due to the involvement of the state constraint, a new kind of penalty functionals is constructed for the pay-off functional. Necessary conditions on the optimality for the problem are given and proven.
期刊：
Journal of Differential Equations,2000年163(2):348-380 ISSN：0022-0396
通讯作者：
Yang, T
作者机构：
City Univ Hong Kong, Dept Math, Kowloon, Hong Kong, Peoples R China.;Acad Sinica, Wuhan Inst Phys & Math, Wuhan 430071, Peoples R China.;SISSA, ISAS, I-34014 Trieste, Italy.;Cent China Normal Univ, Dept Math, Wuhan 430070, Peoples R China.;[Yang, T] City Univ Hong Kong, Dept Math, 83 Tat Chee Ave, Kowloon, Hong Kong, Peoples R China.
通讯机构：
[Yang, T] C;City Univ Hong Kong, Dept Math, 83 Tat Chee Ave, Kowloon, Hong Kong, Peoples R China.
摘要：
In this paper, we study the initial boundary value problem of the following hyperbolic system with relaxation[formula]on the half line R+ with the boundary conditions v(0, t)=v−. When the asymptotic states are stationary wave or rarefaction wave or superposition of these two kind waves, we prove the stability of these wave patterns for small perturbation. The study is motivated by [7] where the asymptotic behavior of solutions to the scalar viscous conservation law with boundary corresponding to rarefaction waves was studied. In our analysis, we do not require (v+, u+) satisfy the equilibrium equation, i.e., u+=f(v+) as in [15].
摘要：
In this paper, we study the following elliptic problem {Delta u + K(x)u(P) = 0 in R-N {u > 0 in R-N (*) where K(x) is a given function in C-alpha(R-n\0) for some fixed alpha epsilon (0, 1), P >1 is a constant. Some existence, monotonicity and asymptotic expansion at infinity of solutions of (*) are discussed. (C) 2000 Academic Press.
摘要：
This paper deals with optimal control problem of parabolic differential equation with two point boundary conditions (in the time variable). The results here extend those in [3] on optimal control of the heat equations. Moreover, the technique used in this paper is based on some smooth approximations of "tangent cones" in the sense of Clarke and some maximal monotone operators.
作者机构：
[Mao, JZ; Li, DY] Cent China Normal Univ, Dept Math, Wuhan 430079, Hubei, Peoples R China.
通讯机构：
[Jingzhong Mao] D;Department of Mathematics, Central China Normal University, Wuhan, Hubei, 430079, People's Republic of China
关键词：
Geodetic graph;Number of edges;Upper bound
摘要：
In this paper we investigate some structural characterizations of geodetic graphs and prove that if G is a central geodetic block on p vertices with diameter d greater than or equal to 3, and each vertex belongs to an induced cycle C2d+1, then the number q of edges equals p or q less than or equal to 1/6 p[p - 1/2(5d + 1) + 8]. Therefore the upper bounds of [3] have been considerably improved. (C) 1999 Elsevier Science B.V. All rights reserved.
作者机构：
[Jia, XH] City Univ Hong Kong, Dept Comp Sci, Kowloon, Hong Kong, Peoples R China.;Cent China Normal Univ, Dept Math, Hubei 430079, Peoples R China.;Univ Qiqihaer, Dept Math, Heilongjiang, Peoples R China.;Chinese Acad Sci, Inst Appl Math, Beijing 100080, Peoples R China.;Univ Minnesota, Dept Comp Sci, Minneapolis, MN 55455 USA.
通讯机构：
[Jia, XH] C;City Univ Hong Kong, Dept Comp Sci, Kowloon, Hong Kong, Peoples R China.
会议名称：
Workshop on Computational Graph Theory
会议时间：
JUL 22-24, 1999
会议地点：
CITY UNIV, HONG KONG, PEOPLES R CHINA
会议主办单位：
City Univ Hong Kong, Dept Comp Sci, Kowloon, Hong Kong, Peoples R China.^Cent China Normal Univ, Dept Math, Hubei 430079, Peoples R China.^Univ Qiqihaer, Dept Math, Heilongjiang, Peoples R China.^Chinese Acad Sci, Inst Appl Math, Beijing 100080, Peoples R China.^Univ Minnesota, Dept Comp Sci, Minneapolis, MN 55455 USA.
摘要：
This paper is concerned with some nonlinear heat equations with initial condition and anti-periodic boundary condition. Also some two-point value nonlinear heat equations with anti-periodic boundary condition are discussed. The existence and uniqueness of the solutions are given. Some asymptotic behaviors of the solutions are studied.
作者机构：
[Xiao, DM; Deng, ZQ] Cent China Normal Univ, Dept Math, Wuhan 430079, Peoples R China.
通讯机构：
[Dongmei, X.] D;Department of Mathematics, Central China Normal University, China
关键词：
absolute stability;two classes;time-varying;nonlinear control system
摘要：
In this paper the authors study two classes of time-varying nonlinear control systems. A few sufficient conditions of absolute stability of these systems were obtained by means of classical analysis and the analogue of the variation of constants formula of nonlinear systems. Moreover, they gave some sufficient conditions of absolute stability in Hurwitz angle for these systems.
摘要：
This paper has completely studied the dynamical properties of a class of epidemiological models, obtained the necessary and sufficient condition for a unique periodic solution which is asymptotically orbitally stable, and the necessary and sufficient conditions for the global asymptotic stability of the positive equilibrium.
期刊：
Numerical Functional Analysis and Optimization,1999年20(1):163-174 ISSN：0163-0563
通讯作者：
Wang, Gengsheng
作者机构：
Huazhong Normal Univ, Dept Math, Wuhan 430079, Peoples R China.;Wuhan Univ, Dept Phys, Wuhan 430072, Peoples R China.;[Chen, SR] Department of Physics, Wuhan University, 430072, Wuhan, China;[Wang, GS] Department of Mathematics, Huazhong Normal University, Wuhan, 430079, China
通讯机构：
Huazhong Normal Univ, China
关键词：
maximum principle;optimal control problems;finite codimension;state constraint
摘要：
The maximum principle for optimal control problems of linear parabolic system with two point state constraint is discussed. Applications to some boundary periodic and distributed control problems are presented.
期刊：
PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS,1999年129(5):925-946 ISSN：0308-2105
通讯作者：
Deng, YB
作者机构：
[Wang, GS; Deng, YB] Huazhong Normal Univ, Dept Math, Wuhan, Peoples R China.
通讯机构：
[Deng, YB] H;Huazhong Normal Univ, Dept Math, Wuhan, Peoples R China.
摘要：
In this paper, we consider the existence of multiple solutions of biharmonic equations boundary value problem, Δ2u = λu + |u|p-2u + f(cursive Greek chi), cursive Greek chi cursive Greek chi ∈ Ω,} u|∂Ω = 0, ∂u/∂n|∂Ω = 0, where Ω is a bounded smooth domain in ℝN, N ≥ 5; λ ∈ ℝ1 is a given constant; p = 2N/(N - 4) is the critical Sobolev exponent for the embedding H0 2(Ω) AA; Lp(Ω); Δ2 = ΔΔ denotes iterated N-dimensional Laplacian; f(cursive Greek chi) is a given function. Some results on the existence and non-existence of multiple solutions for the above problem have been obtained by Ekeland's variational principle and the mountain-pass lemma under some assumptions on f(cursive Greek chi) and N.
摘要：
This work is concerned with analysis and optimal control of a semilinear elliptic partial differential equation involving critical exponent. Some necessary conditions for optimality are given.
期刊：
Calculus of Variations and Partial Differential Equations,1999年8(2):91-107 ISSN：0944-2669
通讯作者：
Chen, Q
作者机构：
[Chen, Q] Mathematics Department, Central China Normal University, Wuhan 430079, China, Mathematics Department, Wuhan University, Wuhan 430079, China
通讯机构：
[Chen, Q ] ;Cent China Normal Univ, Dept Math, Wuhan 430079, Peoples R China.
摘要：
In this paper, we consider the harmonic maps with potential from compact Riemannian manifold with boundary into a convex ball in any Riemannian manifold. We will establish some general properties such as the maximum principles, uniqueness and existence for these maps, and as an application of them, we derive existence and uniqueness result for the Dirichlet problem of the Landau-Lifshitz equations.
作者机构：
Acad Sinica, Inst Math, Beijing 100080, Peoples R China.;Cent China Normal Univ, Dept Math, Wuhan 430079, Peoples R China.;[Zhang, XA] Institute of Mathematics, Academia Sinica, Beijing 100080, China, Department of Mathematics, Central China Normal University, Wuhan 430079, China;[Chen, LS] Institute of Mathematics, Academia Sinica, Beijing 100080, China;[Liang, ZJ] Department of Mathematics, Central China Normal University, Wuhan 430079, China
通讯机构：
[Zhang, X.] I;Institute of Mathematics, Academia Sinica, China
摘要：
In this paper, the authors prove that the flows of homogeneous vector field Q(x) at infinity are topologically equivalent to the flows of the tangent vector field Q T (u) (u ∈ S 2 ) on the sphere S 2 , and show the theorems for the global topological classification of Q(x). They derive the necessary and sufficient conditions for the global asymptotic stability and the boundedness of vector field Q(x), and obtain the criterion for the global topological equivalence of two homogeneous vector fields. Tangent vector field, Invariant cone, Global topological equivalence.
摘要：
We study the Cauchy problem for a set of nonlinear evolution equations, which has been proposed for the investigation of nonlinear interaction between ellipticity and dissipation. The zero equilibrium is linearly stable for coefficients within certain range. We further establish the global existence, nonlinear stability, and optimal decay rate of the solution for coefficients within the same range, though, with suitable restriction to initial data.
作者机构：
[Xiao, DM; Li, WX] Cent China Normal Univ, Dept Math, Wuhan 430079, Peoples R China.
通讯机构：
[Wenxia, L.] D;Department of Mathematics, Central China Normal University, China
关键词：
General;SIERPINSKI;CARPET;DIMENSION;of;measure.;PROBABILITY;MEASURE;dimension of measure;probability measure
摘要：
Let S = Π∞i=1 {0, 1,⋯, r - 1} and R̄ the general Sierpinski carpet. Let μ be the induced probability measure on R̄ of μ̄ on S by φ, where φ is the natural subjection from S onto R̄ and μ̄ is the infinite product probability measure corresponding to probability vector (b0,⋯,br-1) with bi = alogn m-1i/mα. Authors show that dimH μ = CL(μ) = C̄L(μ) = C(μ) = C̄(μ) = α.
作者机构：
[Mao, JZ; Li, DY] Cent China Normal Univ, Dept Math, Wuhan 430079, Peoples R China.
通讯机构：
[Deying, L.] D;Department of Mathematics, Central China Normal University, China
关键词：
GEODETIC;BLOCK;SUBDIVISION;subdivision
摘要：
In this paper authors have obtained a new necessary and sufficient condition for a graph G to be a geodetic graph. Let g : E → Z+ be a function from the set of edges of a graph G to the set of nonnegative integers and let g(G) denote the graph obtained from G by replacing each edge e ∈ E by a suspended arc (path) Pg(e)+2 of length g(e) + 1. and by using this condition, established a criterion for a function g to be a function which can generate a new geodetic block g(G) from a given geodetic block G.
作者机构：
[Xiao, DM; Li, WX] Cent China Normal Univ, Dept Math, Wuhan 430079, Peoples R China.
通讯机构：
[Li, W.] D;Department of Mathematics, Central China Normal University, China
关键词：
Cantor triadic set;Generalized Moran set;Multifractal decomposition, point-wise dimension
摘要：
Let C be the Canter triadic set and let C-alpha = C + alpha = (beta+alpha : beta is an element of C) for -1 less than or equal to alpha less than or equal to 1. Let H-p = (alpha is an element of C : dim(H) (C-alpha boolean AND C) = dim(B) (C-alpha boolean AND C) = (1 - p) log 2/log 3), 0 < p < 1. The authors give the dimensions of C-alpha boolean AND C and H-p In addition the characteristic of H-p is described by means of some measure mu supported on C.
摘要：
In this paper, the author considers a class of complete noncompact Riemannian manifolds which satisfy certain conditions on Ricci curvature and volume comparison. It is shown that any harmonic map with finite energy from such a manifold M into a normal geodesic ball in another manifold N must be asymptotically constant at the infinity of each large end of M. A related existence theorem for harmonic maps is established.
