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asymptotic solutions OF BOUNDARY VALUE PROBLEMS FOR THIRD-ORDER ORDINARY DIFFERENTIAL EQUATIONS WITH TURNING POINTS

Applied Mathematics and Mechanics(English Edition) 2001年第4期22卷 394-403页

作者： JIANG Fu-ru(江福汝) JIN Qi-nian(金其年) Shanghai Institute of Applied Mathematics and Mechanics Shanghai UniversityShanghai 200072 P R China Department of Mathematics Nanjing University Nanjing 210000 P R China

Boundary value problem; for third-order ordinary differential equations with turning points are studied as follows : epsilon gamma ' ' + f(x ; epsilon) gamma ' + g(x ; epsilon) gamma ' +h(x ; epsilon) gamma = 0 (- a <... 详细信息

关键词： boundary value problems ordinary differential equations turning points asymptotic solutions

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asymptotic Behavior of Soliton solutions with a Double Spectral Parameter for Principal Chiral Field

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Communications in Theoretical Physics 2005年第6X期44卷 977-980页

作者： SONG Quan-Fu ZHOU Zi-Xiang School of Mathematical Sciences Fudan University Shanghai 200433 China

The soliton solutions with a double spectral parameter for the principal chiral field are derived by Darboux transformation. The asymptotic behavior of the solutions as time tends to infinity is obtained and the speed... 详细信息

关键词： principal chiral field asymptotic solutions

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solutions of the Generalized Lennard-Jones System

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Acta Mathematica Sinica,English Series 2018年第2期34卷 139-170页

作者： Bowen LIU Yiming LONG Chongchun ZENG Chern Institute of Mathematics Nankai University Chern Institute of Mathematics and LPMC Nankai University School of Mathematics Georgia Institute of Technology

In this paper, we study solution structures of the following generalized Lennard-Jones system in R^n,x（-α/｜x｜α＋2＋β/｜x｜β＋2）xwith 0 〈 α 〈β. Considering periodic solutions with zero angular momentum, we prove that the corre- sponding problem degenerates to I-dimensional and possesses infinitely many periodic solutions which must be oscillating line solutions or constant solutions. Considering solutions with non-zero angular momentum, we compute Morse indices of the circular solutions first, and then apply the mountain pass theorem to show the existence of non-circular solutions with non-zero topological degrees. We further prove that besides circular solutions the system possesses in fact countably many periodic solutions with arbitrarily large topological degree, infinitely many quasi-periodic solutions, and infinitely many asymptotic solutions.

关键词： Generalized Lennard-Jones system mountain pass solutions periodic solutions quasi- periodic solutions asymptotic solutions

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Absorption Rate into a Small Sphere for a Diffusing Particle Confined in a Large Sphere

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Applied Mathematics 2016年第7期7卷 709-720页

作者： Hongyun Wang Hong Zhou Department of Applied Mathematics and Statistics Baskin School of Engineering University of California Santa Cruz CA USA Department of Applied Mathematics Naval Postgraduate School Monterey CA USA

We study the problem of a diffusing particle confined in a large sphere in the n-dimensional space being absorbed into a small sphere at the center. We first non-dimensionalize the problem using the radius of large confining sphere as the spatial scale and the square of the spatial scale divided by the diffusion coefficient as the time scale. The non-dimensional normalized absorption rate is the product of the physical absorption rate and the time scale. We derive asymptotic expansions for the normalized absorption rate using the inverse iteration method. The small parameter in the asymptotic expansions is the ratio of the small sphere radius to the large sphere radius. In particular, we observe that, to the leading order, the normalized absorption rate is proportional to the (n - 2)-th power of the small parameter for .

关键词： Diffusion Equation Brownian Diffusion asymptotic solutions Absorption Rate

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Non-Detection Probability of a Diffusing Target by a Stationary Searcher in a Large Region

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Applied Mathematics 2016年第3期7卷 250-266页

We revisit one of the classical search problems in which a diffusing target encounters a stationary searcher. Under the condition that the searcher’s detection region is much smaller than the search region in which the target roams diffusively, we carry out an asymptotic analysis to derive the decay rate of the non-detection probability. We consider two different geometries of the search region: a disk and a square, respectively. We construct a unified asymptotic expression valid for both of these two cases. The unified asymptotic expression shows that the decay rate of the non-detection probability, to the leading order, is proportional to the diffusion constant, is inversely proportional to the search region, and is inversely proportional to the logarithm of the ratio of the search region to the searcher’s detection region. Furthermore, the second term in the unified asymptotic expansion indicates that the decay rate of the non-detection probability for a square region is slightly smaller than that for a disk region of the same area. We also demonstrate that the asymptotic results are in good agreement with numerical solutions.

关键词： Detection of a Random Target asymptotic solutions Decay of the Non-Detection Probability

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A Note on Differential Equation with a Large Parameter

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Applied Mathematics 2016年第3期7卷 183-192页

作者： S. O. Maliki R. N. Okereke Department of Mathematics Michael Okpara University of Agriculture Umudike Nigeria

We present here asymptotic solutions of equations of the type , where is a large parameter. The Bessel differential equation is considered as a typical example of the above and the solutions are provided as . Furthermore, the behaviour of the solutions as well as the stability of the Bessel ode is investigated numerically as the parameter grows indefinitely.

关键词： ODE asymptotic solutions Bessel Differential Equation Stability MathCAD Solution

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Bifurcation to a corner-like formation in a slender nonlinearly elastic cylinder:asymptotic solution and mechanism

Bifurcation to a corner-like formation in a slender nonlinea...

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第十三届全国非线性振动暨第十届全国非线性动力学和运动稳定性学术会议

作者： HUI-HUI DAI1,2,AND FAN-FAN WANG1 1Department of Mathematics,and 2Liu Bie Ju Center for Mathematical Sciences,City University of Hong Kong,83 TatChee Avenue,Kowloon Tong,Hong Kong,Republic of China

In this paper,we study the corner-like formation in a slender nonlinearly elastic cylinder due to ***,this is a very challenging problem:one needs to study the bifurcation of the nonlinear eld equations(complicated nonlinear partial differential equations)and show that there is a bifurcation leading to a solution with a corner-like *** also aim to obtain the asymptotic expression for this post-bifurcation *** far as we know,there is no available analytical method to obtain the post-bifurcation solution of nonlinear partial differential equation(s).Here we use a novel approach to tackle the present *** a method of coupled series-asymptotic expansions,we manage to derive the normal form equation of the original nonlinear eld equations,which can be written as a singularordinarydifferentialequation(ODE)system(thevectoreldhasa singularityatone point).With welding end conditions,the problem is reduced to study the boundary-value problemofa *** seems thatsucha boundary-value problem ofa singular ODEsyste*** thehelpofphaseplanes,*** there is a vertical singular line in phase planes,which causes the bifurcation to a corner-like *** expression for this post-bifurcation solution is also *** the analyticalresults obtained,we reveal that the coupling effect ofthe materialnonlinearityand geometrical size is the physical mechanism that causes the formation of a corner-like prole.

关键词： nonlinear elasticity bifurcation of nonlinear partial differential equations corner-like prole asymptotic solutions

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