数学物理学报(英文版)

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GENERAL OPEN MAPPING THEOREMS FOR LINEAR TOPOLOGICAL SPACES

丘京辉

数学物理学报(英文版). 1998 (3): 241-248.

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In this paper, the author establishs general open mapping theorems for continuous, weakly continuous, closed and weakly singular linear maps respectively. From these general theorems, he deduces a lot of specific open mapping theorems. which include some well-known theorems and some new interesting results. Particularly the author gives the extensions of Husain's open mapping theorem and Adasch's open mapping theorem.

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ON GLOBAL EXISTENCE AND NONEXISTENCE FOR SOME NONLINEAR PARABOLIC EQUATIONS

王卫东, 张全德

数学物理学报(英文版). 1998 (3): 249-261.

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This paper gives the sufficient and necessary conditions of existence of global solutions and decay estimates of the solutions for the initial boundary value problem of some nonlinear parabolic equations with small initial energy and the nonlinear power less than Sobolev critical value. The existence, nonexistence and the decay estimates of global solutions are considered. The conditions that initial energy is small and nonlinear power is less than Sobolev critical value is imposed.

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BEST LIPSCHITZ CONSTANTS FOR THE BÉZIER NETS AND BERNSTEIN POLYNOMIALS OVER A SIMPLEX

陈发来

数学物理学报(英文版). 1998 (3): 262-270.

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The present paper finds out that the geometric entity which characterizes the best Lipschitz constants for the Bézier nets and Bernstein polynomials over a simplex σ is an angle φ determined by σ, and proves that (1) if f(x) is Lipschitz continuous over σ, i.e., f(x) ∈ Lip_A(α,σ), then both the n-th Bézier net f_n and the n-th Bernstein polynomial B_n(f; x) corresponding to f(x) belong to Lip_B(α,σ), where B=Asec^αφ; and (2) if n-th Bézier net f_n ∈ Lip_A(α,σ), then the elevation Bézier net Ef_n and the corresponding Bernstein polynomial B_n(f,;x) also belong to Lip_A(α,σ). Furthermore, the constant B=Asec^αφ in case (1) is best in some sense.

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AN IRREGULAR OBLIQUE DERIVATIVE PROBLEM FOR SOME NONLINEAR ELLIPTIC EQUATIONS OF SECOND ORDER

闻国椿, 黄沙

数学物理学报(英文版). 1998 (3): 271-277.

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This paper deals the irregular oblique derivative problem for some nonlinear elliptic equations of second order. First a priori estimates of solutions are given, after wards by using the above estimates of solutions and the Schauder fixed-point theorem, the existence of solutions for the above boundary value problems is proved.

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LOCAL AND GLOBAL STABILITY OF INFINITE-HORIZON VARIATIONAL PROBLEM

龚六堂, 费溥生

数学物理学报(英文版). 1998 (3): 278-284.

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This paper presents an existence theorem of the optimal solution for the infintehorizon variational problem with the inclusion constraints on the state variables and velocity variables, give the estimation of the optimal solution. Under some conditions, the authors obtain the local stability and global stability of the stationary solution.

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MONOTONE ITERATIVE TECHNIQUE FOR NONLINEAR NEUTRAL DELAY DIFFERENTIAL EQUATIONS

姜子文, 庄万

数学物理学报(英文版). 1998 (3): 285-292.

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The objective of this paper is to develop monotone techniques for obtaining extremal solutions of initial value problem for nonlinear neutral delay differential equations.

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BIFURCATIONS TO A HETEROCLINIC MANIFOLD WITH NONHYPERBOLIC EQUILIBRIA IN Rⁿ

孙建华, Robert E. Kooij

数学物理学报(英文版). 1998 (3): 293-302.

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The authors study bifurcations from a heteroclinic manifold connecting two non-hyperbolic equilibrium P₀ and P₁ for a n-dimensional dynamical system. They show that under some assumptions, each equilibrium P_i splits into two equilibria P_i and P_i(α), i=0, 1, and find the Melnikov vector conditions assuring the existence of a heteroclinic orbit from P₁ (α) to P₀ (α) along directions that are tangent to the strong unstable (resp.strong stable) manifold of P₁ (α) (resp.P₀(α)). The exponential trichotomy and the unified and geometrical method are used to prove their results.

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ON A CHAIN OF BUTLER GROUPS

李武炎, 张员荣

数学物理学报(英文版). 1998 (3): 303-309.

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This paper is devoted to the examination of a strictly increasing chain of subclasses of Butler groups.

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THE MAXIMUM OF THE γ-MAX-SUBADDITIVE FUNCTIONALS ON A CLASS OF TOPOLOGICAL GROUPS

定光桂

数学物理学报(英文版). 1998 (3): 310-314.

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It is shown that if a "max-subadditive funtional" p(x) defined on some symmetric neighborhood Ū₀ of zero vector θ in a "b.f.-toplological group" X is "upper semi-cotinuous" at a point x₀ ∈ Ū₀, or "lower semi-continuous" in some neighborhood V(x₀)⊂Ū₀ and X is of second category; then p(x) can attain its supremum in Ū₀. And there is a similar conclusion for the γ-max-subadditive functional when its supremum is 0 and if Ū₀ is "pseudo-bounded" set in X.

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THE BLOW-UP PROPERLIES OF SOLUTIONS TO SEMILINEAR HEAT EQUATIONS WITH NEUMANN BOUNDARY CONDITIONS

林支桂

数学物理学报(英文版). 1998 (3): 315-325.

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This paper deals with the blow-up properties of solutions to semilinear heat equation u_t-u_xx=u^p in (0, 1)×(0, T) with the Neumann boundary condition u_x(0, t)=0, u_x(1, t)=1 on[0, T). The necessary and sufficient conditions under which all solutions to have a finite time blow-up and the exact blow-up rates are established. It is proved that the blow-up will occur only at the boundary x=1. The asymptotic behavior near the blow-up time is also studied.

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EXISTENCE, BOUNDEDNESS AND UNIQUENESS OF WEAK SOLUTION FOR THE THERMISTOR PROBLEM WITH MIXED BOUNDARV CONDITIONS

管平

数学物理学报(英文版). 1998 (3): 326-332.

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The thermistor problem is a coupled system of nonlinear PDEs with mixed boundary conditions. The goal of this paper is to study the existence, boundedness and uniqueness of the weak solution for this problem.

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LOWER BOUND NUMBER OF IRREDUCIBLE GRAPHS ON SURMCES

刘莹, 刘彦佩

数学物理学报(英文版). 1998 (3): 333-339.

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Irreducible graphs are those graphs which can hot be embedded on some surface but deleting ally edge of this graph, the resultant graph can be embedded on the surface. This paper characterizes one kind of irreducible graphs and it is shown that the lower bound number of irreducible graphs for the surface of genus n is 2×16ⁿ.

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GLOBAL STRONG SOLUTIONS FOR A CLASS OF BBM-BO TYPE EQUATION

酒全森

数学物理学报(英文版). 1998 (3): 340-347.

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In this paper, the initial value problem for a class of BBM-BO type equation is considered. By means of priori estimates and Galerkin method, the existence and uniqueness of the solution in a suitable Sobolev space are obtained.

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ON THE RELATIVISTIC BOLTZMANN EQUATION

姜正禄

数学物理学报(英文版). 1998 (3): 348-360.

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This paper shows the invalidity of Dudyński and Ekiel-Jezewska's existence proof for the relativistic Boltzmann equation, and proves global existence of mild solutions of its initial value problem with initial data only satisfying the natural bound, i.e., finite mass,"inertia", energy and entropy.

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