Chen, Shukai Li, Zenghu
Published in
Acta Mathematica Scientia

A continuous time and mixed state branching process is constructed by a scaling limit theorem of two-type Galton-Watson processes. The process can also be obtained by the pathwise unique solution to a stochastic equation system. From the stochastic equation system we derive the distribution of local jumps and give the exponential ergodicity in Wass...

Jiang, Xuyong Sun, Hejun Zhao, Peibiao
Published in
Acta Mathematica Scientia

In this paper, we give some rigidity results for complete self-shrinking surfaces properly immersed in ℝ4 under some assumptions regarding their Gauss images. More precisely, we prove that this has to be a plane, provided that the images of either Gauss map projection lies in an open hemisphere or S2(1/2)\S¯+1(1/2)\documentclass[12pt]{minimal} \use...

Chen, Tuowei Zhang, Yongqian
Published in
Acta Mathematica Scientia

We study the initial boundary value problem for the three-dimensional isentropic compressible Navier-Stokes equations in the exterior domain outside a rotating obstacle, with initial density having a compact support. By the coordinate system attached to the obstacle and an appropriate transformation of unknown functions, we obtain the three-dimensi...

Xiao, Yu Xu, Jian Fan, Engui
Published in
Acta Mathematica Scientia

In this paper, we apply Fokas unified method to study the initial boundary value (IBV) problems for nonlinear integrable equation with 3 × 3 Lax pair on the finite interval [0, L]. The solution can be expressed by the solution of a 3 × 3 Riemann-Hilbert (RH) problem. The relevant jump matrices are written in terms of matrix-value spectral functions...

Sun, Guangling Xu, Lu Zhang, Ping
Published in
Acta Mathematica Scientia

In this paper, we prove the uniqueness of the Lp Minkowski problem for q-torsional rigidity with p > 1 and q > 1 in smooth case. Meanwhile, the Lp Brunn-Minkowski inequality and the Lp Hadamard variational formula for q-torsional rigidity are established.

Ke, Xueli Yuan, Baoquan Xiao, Yaomin
Published in
Acta Mathematica Scientia

This paper is concerned with a stability problem on perturbations near a physically important steady state solution of the 3D MHD system. We obtain three major results. The first assesses the existence of global solutions with small initial data. Second, we derive the temporal decay estimate of the solution in the L2-norm, where to prove the result...

Zhou, Jianfeng Tan, Zhong
Published in
Acta Mathematica Scientia

We study the regularity of weak solutions to a class of second order parabolic system under only the assumption of continuous coefficients. We prove that the weak solution u to such system is locally Hölder continuous with any exponent α ∈ (0, 1) outside a singular set with zero parabolic measure. In particular, we prove that the regularity point i...

Gao, Junpei Cui, Haibo
Published in
Acta Mathematica Scientia

We investigate the asymptotic behavior of solutions to the initial boundary value problem for the micropolar fluid model in a half line ℝ+ ≔ (0, ∞). Inspired by the relationship between a micropolar fluid model and Navier-Stokes equations, we prove that the composite wave consisting of the transonic boundary layer solution, the 1-rarefaction wave, ...

Özarslan, Mehmet Ali Yilmaz Yaşar, Banu
Published in
Acta Mathematica Scientia

In this paper, we introduce the Δh-Gould-Hopper Appell polynomials An(xyh)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\mathcal A}_n}(x,y;h)$$\end{document} via h-...

Chen, Hao Yang, Jinyu Liu, Min-Qian
Published in
Acta Mathematica Scientia

In this paper, we propose a new method, called the level-collapsing method, to construct branching Latin hypercube designs (BLHDs). The obtained design has a sliced structure in the third part, that is, the part for the shared factors, which is desirable for the qualitative branching factors. The construction method is easy to implement, and (near)...