Published in Acta Mathematica Scientia
In this article, we establish the exponential time decay of smooth solutions around a global Maxwellian to the non-linear Vlasov–Poisson–Fokker–Planck equations in the whole space by uniform-in-time energy estimates. The non-linear coupling of macroscopic part and Fokker–Planck operator in the model brings new difficulties for the energy estimates,...
Published in Acta Mathematica Scientia
In this article, we study the analytical smoothing effect of Cauchy problem for the incompressible Boussinesq equations. Precisely, we use the Fourier method to prove that the Sobolev H1-solution to the incompressible Boussinesq equations in periodic domain is analytic for any positive time. So the incompressible Boussinesq equations admit exactly ...
Published in Acta Mathematica Scientia
This paper is devoted to studying the existence of positive solutions for the following integral system {u(x)=∫ℝn|x−y|λv−q(y)dy,v(x)=∫ℝn|x−y|λu−p(y)dy,p,q>0,λ∈(0,∞),n≥1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \set...
Published in Acta Mathematica Scientia
In this paper, we consider small perturbations of the KdV-mKdV equation ut=−uxxx+6uux+6u2ux\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${u_t} = - {u_{xxx}} + 6u{u_x}...
Published in Acta Mathematica Scientia
With the help of a radially invariant vector field, we derive inequalities of the Hardy kind, with no boundary terms, for W1,p functions on bounded star domains. Our results are not obtainable from the classical inequalities for W01,p functions. Unlike in W01,p, our inequalities admit maximizers that we describe explicitly.
Published in Acta Mathematica Scientia
In this paper, we present a new hybrid conjugate gradient algorithm for unconstrained optimization. This method is a convex combination of Liu-Storey conjugate gradient method and Fletcher-Reeves conjugate gradient method. We also prove that the search direction of any hybrid conjugate gradient method, which is a convex combination of two conjugate...
Published in Acta Mathematica Scientia
In this paper, we consider the following viscoelastic wave equation with delay |ut|ρutt−Δu−Δutt+∫0tg(t−s)Δu(s)ds+μ1μt(x,t)+μ2μt(x,t−τ)=b|u|p−2u\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-6...
Published in Acta Mathematica Scientia
The Cauchy problem of the generalized Kuramoto-Sivashinsky equation in multi-dimensions (n ≥ 3) is considered. Based on Green’s function method, some ingenious energy estimates are given. Then the global existence and pointwise convergence rates of the classical solutions are established. Furthermore, the Lp convergence rate of the solution is obta...
Published in Acta Mathematica Scientia
Consider the difference Riccati equation xxxx, where A, B, C, D are meromorphic functions, we give its solution family with one-parameter H(f(z))={f0(z),f(z)=(f1(z)−f0(z))(f2(z)−f0(z))Q(z)(f2(z)−f1(z))+(f2(z)−f0(z))+f0(z)}\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{a...
Published in Acta Mathematica Scientia
This article is involved with the asymptotic behavior of solutions for nonlinear hyperbolic system with external friction. The global existence of classical solutions is proven, and Lp convergence rates are obtained. Compared with the results obtained by Hsiao and Liu, better convergence rates are obtained in this article.
