数学物理学报(英文版)

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ANTICIPATING QUADRANT AND SYMMETRIC INTEGRALS IN THE PLANE WITH APPLICATION TO WIENER SPACE

龙红卫

数学物理学报(英文版). 1997 (1): 1-11.

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We introduce anticipating quadrant and symmetric integrals in the plane,and establish the associated chain rules which are the same as the deterministic ones.In particular, we deduce the relation between quadrant integrals, symmetric integral,and Skorohod integral with respect to two-parameter Wiener processes.

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ON HOMOGENEOUS RIEMANN BOUNDARY VALUE PROBLEMS OF HIGHER DEGREE

路见可

数学物理学报(英文版). 1997 (1): 12-21.

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General solution for homogeneous Riemann problems of higher degree is considered. By introducing the concept of loop as wen as cross-point, the problem is solved in detail for the quadratic case. The cubic and the quartic ones are also analysed.

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THE BIDIMENSIONAL EVOLUTIONARY BOUSSINESQ-STEFAN PROBLEM WITH CONTINUOUS EXTRACTION

易法槐

数学物理学报(英文版). 1997 (1): 22-34.

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In this paper we consider an evolutionary continuous casting problem with convection
∂^tx+b∂_yx-△k(u)+v·▽u=0 coupled with Stokes equation in the liquid phase
∂_tv-ν△v+▽p=f(u) The mixed boundary condition is put on temprature. The existence of a weak solution is obtained by using methods of regularization, temperature dependent penalty form in the Stokes equation and compact arguments.

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PERIODIC BOUNDARY VALUE PROBLEMS FOR NONLINEAR IMPULSIVEINTEGRODIFFERENTIAL EQUATIONS OF MIXED TYPE IN BANACH SPACES

韦忠礼

数学物理学报(英文版). 1997 (1): 35-43.

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In this paper, the author obtains an existence theorem of minimal and maximal solutions for the periodic boundary value problems of nonlinear impulsive integrodifferential equations of eded type in Banach space by means of the monotone iterative technique and cone theory based on a comparison result.

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THE SINGULARLY PERTURBED BOUNDARY VALUE PROBLEMS FOR HIGHER ORDER SEMILINEAR ELLIPTIC EQUATIONS

莫嘉琪, 许玉兴

数学物理学报(英文版). 1997 (1): 44-50.

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In this paper a singular perturbation of boundary value problem for elliptic partial differential equations of higher order is considered by using the differential inequalities. The uniformly valid asymptotic expansion in entire region is obtained.

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ON LEVIN TYPE COMPARISON THEOREMS FOR CERTAIN SECOND ORDER DIFFERENTIAL EQUATIONS

B. G. Pachpatte

数学物理学报(英文版). 1997 (1): 51-55.

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In this paper we establish Levin type comparison theorems for certain second order differential equations. The results obtained here generalize and extend some of the earlier ones related to the Levin's comparison theorems.

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MULTIPLE BOUNDARY LAYER PHENOMENA OF THE SOLUTION OF NONLINEAR HIGHER ORDER ELLIPTIC EQUATIONS WITH PERTURBATION BOTH IN BOUNDARY AND IN OPERATOR

林苏榕, 林宗池

数学物理学报(英文版). 1997 (1): 56-63.

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In this paper, we reveal the multiple boundary layer phenomena of the solution of nonlinear higher order elliptic equations with perturbation both in boundary and in operator, and provide a method to find uniformly valid asymptotic solution of arbitrary order for these types of problems.

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ON THE LIMITABILITY OF SOLUTIONS OF SOME DIFFERENCE EQUATIONS

L. Rempulska, B. Szmanda

数学物理学报(英文版). 1997 (1): 64-68.

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We investigate limitability by the Cesáro (C, 1) and the Abel (A) methods of solutions of some third and fourth order difference equations. Also some results contained in[2],[3] are improved.

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AUTOMATIC AUGMENTED GALERKIN ALGORITHMS FOR FREDHOLM INTEGRAL EQUATIONS OF THE FIRST KIND

S. Abbasbandy, E. Babolian

数学物理学报(英文版). 1997 (1): 69-84.

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In recent papers, Babolian & Delves^[2] and Belward^[3] described a Chebyshev series method for the solution of first kind integral equations. The expansion coefficients of the solution are determined as the solution of a mathematical programming problem.The method involves two regularization parameters, C_f and r, but values assigned to these parameters are heuristic in nature. Essah & Delves^[7] described an algorithm for setting these parameters automatically, but it has some difficulties. In this paper we describe three iterative algorithms for computing these parameters for singular and non-singular first kind integral equations. We give also error estimates which are cheap to compute. Finally, we give a number of numerical examples showing that these algorithms work well in practice.

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CONVERGENCE ANALYSIS AND MRALLEL IMPLEMENTION FOR THE DIRECTED GRAPH-ALGORITHM

方云兰, 郑慧娆, 费浦生

数学物理学报(英文版). 1997 (1): 85-90.

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In this paper we discuss the convergence of the directed graph-algorithm for solving a kind of optimization problems where the objective and subjective functions are all separable, and the parallel implementation process for the directed graph-algorithm is introduced.

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H¹ SOLUTIONS FOR A CLASS OF SEMILINEAR PARABOLIC SYSTEMS

严国政

数学物理学报(英文版). 1997 (1): 91-96.

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In this paper, we consider the Cauchy problem or a class of semilinear parabolic system. Firstly, we obtain the local existence of solutions of (1.1),(1.2) in H¹ (R¹), and then we prove the global existence of the solutions in H¹ through a prioriestimate.

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HOW TO CONSTRUCT LAX REPRESENTATION FOR CONSTRAINED FLOWS OF THE BOUSSINESQ HIERARCHY VIA ADJOINT REPRESENTATIONS

曾云波

数学物理学报(英文版). 1997 (1): 97-107.

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By using the constraint relating potential and eigenfunctions, the decomposition of each equation in the Boussinesq hierarchy into two commuting finite-dimensional integrable Hamiltonian system (FDIHS) is presented. A method to construct the Lax representations for both x-and t_n-constrained flows via reduction of the adjoint representations of the auxiliary linear problems is developed.

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SMOOTHNESS OF INERTIAL MANIFOLD UNDER TIME DISCRETIZATION

马逸尘, 胡常兵

数学物理学报(英文版). 1997 (1): 108-120.

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In this paper we discuss the smoothness of inertial manifolds under time discretization. By the fibre contract principle, see Section 4, we obtain a sufficient condition for C^k(k ≥ 1) inertial manifolds. In view of the numerical computation for dissipative nonlinear evolution equations, it is more important to consider the discretized case than continuous case^[3].

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