Wang, Weike Xue, Rui
Published in
Acta Mathematica Scientia

In this paper, we study a semilinear Timoshenko system with heat conduction having two damping effects. The observation that two damping effects might lead to smaller decay rates for solutions in comparison to one damping effect is rigorously proved here in providing optimality results. Moreover, the global well-posedness for small data is presente...

Peng, Zhigang Obradović, Milutin
Published in
Acta Mathematica Scientia

Let A\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\cal A}$$\end{document} denote the family of all analytic functions f(z) in the unit disk D\documentclass[12pt]{mi...

Liu, Kepan Yang, Yunrui Yang, Yang
Published in
Acta Mathematica Scientia

By using the weighted-energy method combining continuation method, the exponential stability of monostable traveling waves for a delayed equation without quasimonotonicity is established, including even the slower waves whose speed are close to the critical speed. Particularly, the nonlinearity is nonlocal in the equation and the initial perturbati...

Zhang, Danli Xu, Huiming Wang, Jianfei
Published in
Acta Mathematica Scientia

Let λG(z)∣dz∣ be the hyperbolic metric on a simply connected proper domain G ⊂ ℂ containing the origin, and let ∥ · ∥j be the Banach norms of ℂnj\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{...

Gao, Zhensheng Liang, Yan Tan, Zhong
Published in
Acta Mathematica Scientia

The purpose of this work is to investigate the initial value problem for a general isothermal model of capillary fluids derived by Dunn and Serrin [12], which can be used as a phase transition model. Motivated by [9], we aim at extending the work by Danchin-Desjardins [11] to a critical framework which is not related to the energy space. For small ...

El Baraka, Azzeddine Toumlilin, Mohamed
Published in
Acta Mathematica Scientia

This paper concerns the Cauchy problem of the 3D generalized incompressible magneto-hydrodynamic (GMHD) equations. By using the Fourier localization argument and the Littlewood-Paley theory, we get local well-posedness results of the GMHD equations with large initial data (u0, b0) belonging to the critical Fourier-Besov-Morrey spaces ℱN˙p,λ,q1−2α+3...

Tsai, Dong-Ho Wang, Xiaoliu
Published in
Acta Mathematica Scientia

We use two simple methods to derive four important explicit graphical solutions of the curve shortening flow in the plane. They are well-known as the circle, hairclip, paperclip, and grim reaper solutions of the curve shortening flow. By the methods, one can also see that the hairclip and the paperclip solutions both converge to the grim reaper sol...

Ding, Shijin Huang, Bingyuan Li, Quanrong
Published in
Acta Mathematica Scientia

We prove the global existence of classical solutions to a fluid-particle interaction model in ℝ3, namely, compressible Navier-Stokes-Smoluchowski equations, when the initial data are close to the stationary state (ρ*, 0, η*) and the external potential satisfies the smallness assumption. Furthermore, optimal decay rates of classical solutions in H3-...

Lan, Shuangting Chen, Zongxuan
Published in
Acta Mathematica Scientia

Let c be a nonzero constant and f(z) be a transcendental meromorphic function of finite order. Under some conditions, we study the relationships between the exponent of convergence of fixed points of f(z), its shift f(z + c) and forward differences Δcnf(z), n ∈ ℕ+.

Sun, Qingyou Lu, Yunguang Klingenberg, Christian
Published in
Acta Mathematica Scientia

In this article, we study the global L∞ entropy solutions for the Cauchy problem of system of isentropic gas dynamics in a divergent nozzle with a friction. Especially when the adiabatic exponent γ = 3, we apply for the maximum principle to obtain the L∞ estimates w(ρδ,ε, uδ,ε) ≤ B(t) and z(ρδ,ε, uδ,ε) ≤ B(t) for the viscosity solutions (ρδ,ε, uδ,ε...