Published in Acta Mathematica Scientia
In this article, we study multivariate approximation defined over weighted anisotropic Sobolev spaces which depend on two sequences a = {aj}j≥1 and b = {bj}j≥1 of positive numbers. We obtain strong equivalences of the approximation numbers, and necessary and sufficient conditions on a, b to achieve various notions of tractability of the weighted an...
Published in Acta Mathematica Scientia
In this article we study the two-dimensional complete λ-translators immersed in the Euclidean space ℝ3 and Minkovski space ℝ13. We obtain two classification theorems: one for two-dimensional complete λ-translators x: M2 → ℝ3 and one for two-dimensional complete space-like λ-translators x: M2 → ℝ13, with a second fundamental form of constant length....
Published in Acta Mathematica Scientia
The theory of increasing and convex-along-rays (ICAR) functions defined on a convex cone in a real locally convex topological vector space X was already well developed. In this paper, we first examine abstract convexity of increasing plus-convex-along-rays (IPCAR) functions defined on a real normed linear space X. We also study, for this class of f...
Published in Acta Mathematica Scientia
In this article we consider the compressible viscous magnetohydrodynamic equations with Coulomb force. By spectral analysis and energy methods, we obtain the optimal time decay estimate of the solution. We show that the global classical solution converges to its equilibrium state at the same decay rate as the solution of the linearized equations.
Published in Acta Mathematica Scientia
In this paper, we study the coupled system of Kirchhoff type equations {−(a+b∫ℝ3|∇u|2dx)Δu+u=2αα+β|u|α−2u|v|β,x∈ℝ3,−(a+b∫ℝ3|∇v|2dx)Δv+v=2βα+β|u|α|v|β−2v,x∈ℝ3,u,v∈H1(ℝ3),\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \se...
Published in Acta Mathematica Scientia
This article is devoted to studying the initial-boundary value problem for an ideal polytropic model of non-viscous and compressible gas. We focus our attention on the outflow problem when the flow velocity on the boundary is negative and give a rigorous proof of the asymptotic stability of both the degenerate boundary layer and its superposition w...
Published in Acta Mathematica Scientia
In this paper, a stochastic multi-group AIDS model with saturated incidence rate is studied. We prove that the system is persistent in the mean under some parametric restrictions. We also obtain the sufficient condition for the existence of the ergodic stationary distribution of the system by constructing a suitable Lyapunov function. Our results i...
Published in Acta Mathematica Scientia
In this paper, we investigate the λ-nuclearity in the system of completely 1-summing mapping spaces (Π1(·, ·), π1). In Section 2, we obtain that ℂ is the unique operator space that is nuclear in the system (Π1(·, ·), π1). We generalize some results in Section 2 to λ-nuclearity in Section 3.
Published in Acta Mathematica Scientia
In this paper, the Cauchy problem for the two layer viscous shallow water equations is investigated with third-order surface-tension terms and a low regularity assumption on the initial data. The global existence and uniqueness of the strong solution in a hybrid Besov space are proved by using the Littlewood-Paley decomposition and Friedrichs’ regu...
Published in Acta Mathematica Scientia
We show in this work that the limit in law of the cross-variation of processes having the form of Young integral with respect to a general self-similar centered Gaussian process of order β ∈ (1/2, 3/4] is normal according to the values of β. We apply our results to two self-similar Gaussian processes: the subfractional Brownian motion and the bifra...
