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	1. Decay estimates for dissipative wave equations in inhomogeneous media
	JI Shu-Guan
	Mathematics 16 June 2016
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	Abstract:This paper is concerned with the long time behavior of one-dimensional dissipativewave equation with $x$-dependent coefficients $u(x)y_{tt}-(u(x)y_x)_x+a(x)y_t=0$. Such a model arises from the vibrations of an inhomogeneous string and the propagationof seismic waves in nonisotropic media subject to a viscous damping. Meanwhile, it is also a natural reduction model for the $n$-dimensional wave equation in inhomogeneous radially symmetric media.By using the multiplier method, we establish the power decay estimates for the energy and the $L^2$-norm of solutions.
	TO cite this article:JI Shu-Guan. Decay estimates for dissipative wave equations in inhomogeneous media[OL].[16 June 2016] http://en.paper.edu.cn/en_releasepaper/content/4697305


	2. Breathers of discrete one-dimensional nonlinear Schr
	JI Shu-Guan, WANG Zhen-Hua
	Mathematics 16 June 2016
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	Abstract:The nonlinear Schr"odinger equation arises in several areas of physics, such as opticsor quantum mechanics. In recent years, the discrete nonlinear Schr"odingerequation became a strong focal point. This paper is concerned with the breathers of discreteone-dimensional nonlinear Schr"odinger equations in inhomogeneousmedia. By using a constrained minimization approach known as theNehari variational principle or the Nehari manifold approach, weobtain the existence of nontrivial breathers.
	TO cite this article:JI Shu-Guan, WANG Zhen-Hua. Breathers of discrete one-dimensional nonlinear Schr[OL].[16 June 2016] http://en.paper.edu.cn/en_releasepaper/content/4697308

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	3. A Singular algorithm for polynomial iterative roots
	YU Zhiheng, ZHANG Weinian
	Mathematics 24 May 2016
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	Abstract:Based on the theory of minimal irreducible decomposition and thecomputer algebra system {it Singular}, we give an algorithm which can be used to find the simplest algebraicrelations among coefficients polynomials of degree $m^n$ for these polynomials having the $n$-th iterative roots of polynomial form.Moreover, using the algorithm, the explicit expressions of the iterative roots will be given.Furthermore, applying the algorithm we obtain the polynomial quadratic iterative roots of polynomialsof degree 9 and 16.
	TO cite this article:YU Zhiheng, ZHANG Weinian. A Singular algorithm for polynomial iterative roots[OL].[24 May 2016] http://en.paper.edu.cn/en_releasepaper/content/4693828


	4. An analogue of the break-even concentration of a chemostat model in a stochastic environment
	Chunjuan Zhu
	Mathematics 17 February 2016
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	Abstract: In this paper, we get the analogue which is identified as the break-even concentration of the stochastic chemostat mode. If the analogue is bigger than the input concentration of the nutrient, the microorganism is extinct in the chemostat; if the analogue is less than the input concentration of the nutrient, the microorganism is persistent in the chemostat. If the noise of microorganism is big enough, the microorganism is always extinct irrespectively the noise.
	TO cite this article:Chunjuan Zhu. An analogue of the break-even concentration of a chemostat model in a stochastic environment[OL].[17 February 2016] http://en.paper.edu.cn/en_releasepaper/content/4678362


	5. orbital shadowing for $3$-flows
	GAN Shaobo,LI Ming
	Mathematics 31 December 2015
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	Abstract:It is called that a flow has the orbital shadowing propertyif for any $arepsilon>0$ there is $d>0$ such that, for any $d$-pseudoorbit $g(t)$ there exists an orbit $Orb(x)$ satisfying $dh(overline{g(t)},overline{Orb(x)})<arepsilon$. In this paper, it shows that the $C^1$-interior of the set of $3$-dimensional flows having the orbital shadowing property is contained in the set of $Omega$-stable $3$-flows.
	TO cite this article:GAN Shaobo,LI Ming. orbital shadowing for $3$-flows[OL].[31 December 2015] http://en.paper.edu.cn/en_releasepaper/content/4673510


	6. Weakly tracking of vector fields on oriented surfaces
	LI Ming,LIU Zhongjie
	Mathematics 31 December 2015
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	Abstract:It is called that a vector field has the weakly shadowing propertyif for any (arepsilon>0) there is (d>0) such that each (d)-pseudoorbit is contained in the (arepsilon)-neighborhood of an exact orbit.In this paper it shows that on an oriented smoothly closed surface, a vector field is in the (C^1) interior of the set of vectorfields satisfying the weakly shadowing property if and only if it is structurally stable.
	TO cite this article:LI Ming,LIU Zhongjie. Weakly tracking of vector fields on oriented surfaces[OL].[31 December 2015] http://en.paper.edu.cn/en_releasepaper/content/4673507


	7. Variational approach toa class of second order Hamiltonian systems with impulsiveeffects
	ZHOU Jian-Wen,WANG Yan-Ning
	Mathematics 06 November 2015
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	Abstract:In this paper, we present a recent approach via variational methodsand critical point theory to obtain the existence and multiplicityof periodic solutions for the second order Hamiltonian system withimpulsive effects. By establishing a proper variational setting,one multiplicity results is obtained.Finally, one examples is presented to illustrate the feasibilityand effectiveness of our results.
	TO cite this article:ZHOU Jian-Wen,WANG Yan-Ning. Variational approach toa class of second order Hamiltonian systems with impulsiveeffects[OL].[ 6 November 2015] http://en.paper.edu.cn/en_releasepaper/content/4660449


	8. Global attractors for nonlinear parabolic equations with irregular data
	Chai Xiaojuan,Niu Wei-Sheng
	Mathematics 10 October 2015
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	Abstract:This paper is concerned with the large time behavior of solutions to a class of nonlinear parabolic equations with irregular data. Under properassumptions, we prove the existence and uniqueness of the entropy solution to the problem. Then we establish some regularity results on the solution, by which we prove the existence of a global attractor for the solution semigroup
	TO cite this article:Chai Xiaojuan,Niu Wei-Sheng. Global attractors for nonlinear parabolic equations with irregular data [OL].[10 October 2015] http://en.paper.edu.cn/en_releasepaper/content/4657289


	9. Chaos and control of a generalized higher-order nonlinearSchr
	Li Min, Lei Wang, Feng-HuaQi
	Mathematics 25 August 2015
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	Abstract:The nonlinear dynamics of a generalized higher-ordernonlinear Schr"{o}dinger (HNLS) equation with a periodic externalperturbation is investigated numerically. Via the phase planeanalysis, it's found that both the homoclinic orbits andheteroclinic orbits can exist for the unperturbed HNLS equationunder certain conditions. Moreover, under the effect of the periodicexternal perturbation, the quasi-periodic bifurcations arise and canevolve into the chaos. The dynamical responses of the perturbed HNLSequation with regard to the perturbation strength are simulatedthrough the bifurcation diagrams, maximum Lyapunov exponents andphase portraits, which further prove the existence of the chaos forthe HNLS equation with a periodic external perturbation.Furthermore, two methods are used to control the chaos effectively,which can make the chaotic motions evolve into the stablequasi-periodic orbits. Those studies are helpful to reveal thedynamical properties of the HNLS equation.
	TO cite this article:Li Min, Lei Wang, Feng-HuaQi. Chaos and control of a generalized higher-order nonlinearSchr[OL].[25 August 2015] http://en.paper.edu.cn/en_releasepaper/content/4653119


	10. On the limit quasi-shadowing property
	Fang Zhang, Yunhua Zhou
	Mathematics 10 April 2015
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	Abstract:The paper study the limit quasi-shadowing property for diffeomorphisms.This paper prove that any quasi-partially hyperbolic pseudoorbit ${x_{i},n_{i}}_{iin mathbb{Z}}$ can be $mathcal{L}^p$-, limit and asymptotic quasi-shadowed by a points sequence ${y_{k}}_{kin mathbb{Z}}$.Moreover, this paper also investigate the $mathcal{L}^p$-, limit and asymptotic quasi-shadowing properties for partially hyperbolic diffeomorphisms which are dynamically coherent.
	TO cite this article:Fang Zhang, Yunhua Zhou. On the limit quasi-shadowing property[OL].[10 April 2015] http://en.paper.edu.cn/en_releasepaper/content/4638485

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