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运用了初始层函数构造了一类非线性奇摄动抛物型方程初值问题解的渐近展开式,并证明了该展开式达到任意精度的一致有效性. 相似文献
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In this paper we consider zero-relaxation limits for periodic smooth solutions of Euler–Maxwell systems. For well-prepared initial data, we propose an approximate solution based on a new asymptotic expansion up to any order. For ill-prepared initial data, we construct initial layer corrections in an explicit way. In both cases, the asymptotic expansions are valid in time intervals independent of the relaxation time and their convergence is justified by establishing uniform energy estimates. 相似文献
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《Journal of Computational and Applied Mathematics》2002,148(2):323-339
We describe a new uniform asymptotic expansion for the incomplete gamma function Γ(a,z) valid for large values of z. This expansion contains a complementary error function of an argument measuring transition across the point z=a (which is different from that in the well-known uniform expansion for large a of Temme), with easily computable coefficients that do not involve a removable singularity at z=a. Our expansion is, however, valid in a smaller domain of the parameters than that of Temme. Numerical examples are given to illustrate the accuracy of the expansion. 相似文献
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一类双参数三阶半线性方程边值问题的奇摄动 总被引:2,自引:0,他引:2
研究一类双参数三阶半线性方程边值问题的奇摄动,讨论了摄动解随两参数的不同量级所呈现的不同性态的边界层现象,并给出了解的一致有效的渐近展开式. 相似文献
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含双参数的三阶非线性两点边值问题的套层解(英文) 总被引:1,自引:0,他引:1
对含双参数且有套层解的一类三阶非线性微分方程的边值问题的渐近解做了估计 ,得到了任意次近似的一致有效的渐近展开式 . 相似文献
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David M. Bradley Ramesh C. Gupta 《Annals of the Institute of Statistical Mathematics》2003,55(1):217-226
In survival or reliability studies, the mean residual life or life expectancy is an important characteristic of the model.
Here, we study the limiting behaviour of the mean residual life, and derive an asymptotic expansion which can be used to obtain
a good approximation for large values of the time variable. The asymptotic expansion is valid for a quite general class of
failure rate distributions—perhaps the largest class that can be expected given that the terms depend only on the failure
rate and its derivatives. 相似文献
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Singularperturbationofnonlinearboundaryvalueproblemswhichhavedoubleboundarylayerpropertieswerediscussedbysomeauthorsusingthemethodofdifferentialinequali ties[1 ] -[3 ] .Nonlinearboundaryvalueproblemswhichhavenotdoubleboundarylayerpropertieswerediscussedbysomeauthorsusingthemethodofthefixed_pointtheorem[4] -[6 ] .Inthispa perwewillusethefixed_pointtheoremtodiscussthethirdorderdifferentialequationswhichhavedoubleinitiallayer.Weconsiderthefollowingproblem .ε4y =h(t,y,εy′,ε2 y″,ε) ,t∈ [0 ,T… 相似文献
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本文借助不动点原理 ,对二阶拟线性方程的边值问题的渐近解做了估计 ,得到了包括边界层在内的任意次近似的一致有效的渐近展开式 相似文献
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本文利用多重尺度法研究环形薄板在中面压力和横向负荷联合作用下的屈曲问题,得到了解的N阶一致有效渐近展开式.通过实例考察,我们看到用多重尺度法所得的渐近展开式与精确解的渐近展开是完全一致的. 相似文献
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In this article,the interior layer for a second order nonlinear singularly perturbed differential-difference equation is considered.Using the methods of boundary function and fractional steps,we constr... 相似文献
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Considerasingularlyperturbedproblemforhigherorderselnilinearequationswhereeisasmallpositiveparameter,ndenotesaboundedregioninRe,whereonsignifiesasmoothboundaryofn,misaintegerandjk,gi,k,j=0,'',in--1,aresufficientlysmoothfunctionswithregardtotheirvariablesincorrespondenceranges.Modealwiththesingularperturbationforthesecondorder'ellipticequations[1],[2],thefourthorderequations[3]l[4]andaclassofhigherorderequations[5].Inthispaperttheauthorsconsiderthesingularperturbationforevenmoregeneralhigheror… 相似文献
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本文研究某类二阶非线性向量微分方程初值问题ε'x"=f(t,x,x',ε),x(0,ε)=a,x'(0,ε)=β的奇摄动,其中r>0为任意常数,ε>0为小参数,x,f,α,β∈Rn.在适当的假设下,利用多参数展开法和对角化技巧,证得摄动问题解的存在和导出解的高阶的一致有效渐近展开式. 相似文献
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Brice Camus 《Journal of Mathematical Analysis and Applications》2008,341(2):1170-1180
We study the semi-classical trace formula at a critical energy level for a Schrödinger operator on Rn. We assume here that the potential has a totally degenerate critical point associated to a local minimum. The main result, which computes the contribution of this equilibrium, is valid for all time in a compact and establishes the existence of a total asymptotic expansion whose top order coefficient depends only on the germ of the potential at the critical point. 相似文献
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本文利用两变量展开直接构造边界层项的方法,讨论了一类二阶微分差分方程边值问题的奇摄动解,构造了形式渐近解,作出了余项估计,从而证明了解的存在性. 相似文献