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)...
Published in Acta Mathematica Scientia
Given n ≥ 2 and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha > \tfrac{1}{2}$$\end{document}, we obtained an improved upbound of Hausdorff’s dimension of the f...
Published in Acta Mathematica Scientia
The goal of this paper is to study a mathematical model of a nonlinear static frictional contact problem in elasticity with the mixed boundary conditions described by a combination of the Signorini unilateral frictionless contact condition, and nonmonotone multivalued contact, and friction laws of subdifferential form. First, under suitable assumpt...
Published in Acta Mathematica Scientia
In this paper, we consider the following new Kirchhoff-type equations involving the fractional p-Laplacian and Hardy-Littlewood-Sobolev critical nonlinearity: \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\o...
Published in Acta Mathematica Scientia
Let 0 0 for all s, t ≥ 0. The main technique we use is the method of moving spheres in integral forms. Since our assumptions are more general than those in the previous literature, some new ideas are introduced to overcome this difficulty.
Published in Acta Mathematica Scientia
We are concerned with the shock diffraction configuration for isothermal gas modeled by the conservation laws of nonlinear wave system. We reformulate the shock diffraction problem into a linear degenerate elliptic equation in a fixed bounded domain. The degeneracy is of Keldysh type—the derivative of a solution blows up at the boundary. We establi...
