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...
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...
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...
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...
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.
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...
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...
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, ...
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-...
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)...
