数学物理学报(英文版)

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1. THE HILBERT BOUNDARY VALUE PROBLEM FOR GENERALIZED ANALYTIC FUNCTIONS IN CLIFFORD ANALYSIS

司中伟, 杜金元

数学物理学报(英文版) 2013, 33 (2): 393-403. DOI: 10.1016/S0252-9602(13)60006-5

摘要（73846）

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Let R_0,n be the real Clifford algebra generated by e₁, e₂, … , e_n satisfying e_ie_j +e_je_i = −2δ_ij , i, j = 1, 2, … , n. e₀ is the unit element. Let Ω be an open set. A function f is called left generalized analytic in Ω if f satisfies the equation

Lf = 0, (0.1)
where
L = q₀e₀∂x₀ + q₁e₁∂x₁ + … + q_ne_n∂x_n,
q_i > 0, i = 0, 1, … , n. In this article, we first give the kernel function for the generalized analytic function. Further, the Hilbert boundary value problem for generalized analytic functions in Rⁿ⁺¹₊ will be investigated.

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2. TWO-DIMENSIONAL RIEMANN PROBLEMS: FROM SCALAR CONSERVATION LAWS TO COMPRESSIBLE EULER EQUATIONS

李杰权, 盛万成, 张同, 郑玉玺

数学物理学报(英文版) 2009, 29 (4): 777-802. DOI: 10.1016/S0252-9602(09)60070-9

摘要（2068）

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In this paper we survey the authors’ and related work on two-dimensional Rie-mann problems for hyperbolic conservation laws, mainly those related to the compressible Euler equations in gas dynamics. It contains four sections: 1. Historical review. 2. Scalar conservation laws. 3. Euler equations. 4. Simplified models.

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3. A CASE STUDY IN THE APPLICATION OF SUPERSATURATED DESIGNS TO COMPUTER EXPERIMENTS

刘民千; 方开泰

数学物理学报(英文版) DOI: 10.1016/S0252-9602(06)60085-4

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4. ON THE 3D VISCOUS PRIMITIVE EQUATIONS OF THE LARGE-SCALE ATMOSPHERE

郭柏灵, 黄代文

数学物理学报(英文版) 2009, 29 (4): 846-866. DOI: 10.1016/S0252-9602(09)60074-6

摘要（1956）

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This paper is devoted to considering the three-dimensional viscous primitive equations of the large-scale atmosphere. First, we prove the global well-posedness for the primitive equations with weaker initial data than that in [11]. Second, we obtain the existence of smooth solutions to the equations. Moreover, we obtain the compact global attractor in V for the dynamical system generated by the primitive equations of large-scale
atmosphere, which improves the result of [11].

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5. BLOW-UP AND GLOBAL EXISTENCE FOR A COUPLED SYSTEM OF DEGENERATE PARABOLIC EQUATIONS IN A BOUNDED DOMAIN

穆春来; 胡学刚; 李玉环; 崔泽键

数学物理学报(英文版)

摘要（1871）

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This article deals with the conditions that ensure the blow-up
phenomenon or its absence for solutions of the system
u_t=△ u^l+u^p₁v^q₁ and v_t=△ v^m+u^p₂v^q₂ with homogeneous Dirichlet boundary conditions. The results depend crucially on the sign of the difference p₂q₁-(l-p₁)(m-q₂), the initial data, and the domain $\Omega$.

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