共查询到20条相似文献,搜索用时 15 毫秒
1.
叶耀军 《数学物理学报(B辑英文版)》2005,25(4):703-709
The author considers the global existence and global nonexistence of the initial-boundary value problem for some degenerate hyperbolic equation of the form utt- div(|▽u|p-2▽u)= |u|mu, (x,t) ∈ [0, ∞) ×Ωwith p > 2 and m > 0. He deals with the global solutions by D.H.Sattinger's potential well ideas. At the same time, when the initial energy is positive, but appropriately bounded,the global nonexistence of solutions is verified by using the analysis method. 相似文献
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带阻尼项的Euler方程组初边值问题的整体解 总被引:2,自引:0,他引:2
本文研究了一维带阻尼项的Euler方程组初边值问题的齐次Dirichlet边值情形.当初值在平衡解附近小扰动时,本文得到了时间整体解的存在唯一性,而且当时间趋于无穷时,此解趋于平衡解. 相似文献
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In this paper, by using Leray-Schauder degree theory, we establish the existence and uniqueness theorems for a kind of fourth-order nonlinear two-point boundary value problem. 相似文献
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A global existence theorem is established for an initial-boundary value problem,with time-dependent boundary data,arising in a lumped parameter model of pulse combustion; the model in question gives ri... 相似文献
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The authors deal with the Cauchy problem with small initial data for the nonlinear elastodynamic system. The almost global existence of solution to this problem is proved in a simpler way and a lower bound for the lifespan of solutions is given. 相似文献
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非凸单个守恒律初边值问题的整体弱熵解的构造 总被引:4,自引:0,他引:4
本文研究具有两段常数的初始值和常数边界值的非凸单个守恒律的初边值问题.在流函数具有一个拐点的条件下,由相应的初始值问题弱熵解的结构和Bardos-Leroux-Nedelec提出的边界熵条件,给出初边值问题整体弱熵解的一个构造方法,澄清弱熵解在边界附近的结构.与严格凸的单个守恒律初边值问题相比,非凸单个守恒律初边值问题的弱熵解中包括下列新的相互作用类型:一个接触或非接触激波碰到边界,边界弹回一个非接触激波. 相似文献
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1IntroductionThebasicequationinsemiconductorkinetictheoryistheBoItzmannEquation.Iftherelevantphysicsconstantsaretakenasone,theBoltzmannEquationin3D,undertheattractforce,canbewrittenas:o,f vV.f-E.V.f=Q(f),xER',vER',t>o,(1.1)wheref(t,x,v)isadistributionfunction,itrepresentsthefractionofoccupiedstatesattimetE[o,oo),atthepoint(x,v)eR'xR3oftheposition-velocityspace.E(f,x)ER'istheelectricfield-IfthepotentialcorrespondingtotheelectricfieldE(f,x)isdenotedbyV(t,x),thenAndV(t,x)satisfiesthePoi… 相似文献
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Si Xin 《偏微分方程(英文版)》2008,21(4):377-383
Existence and extinction in finite time of global weak solutions for the problem (P) are proved. 相似文献
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n阶非线性常微分方程两点及三点边值问题解的存在性的进一步结果 总被引:6,自引:0,他引:6
本文利用上、下解方法讨论了n阶非线性常微分方程y^(n)=f(t,y,y‘…,y^(n-1))满足下列非线性边界条件的边值问题解的存在性。 相似文献
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具有阻尼项的非线性波动方程的初值问题 总被引:2,自引:0,他引:2
本文研究具有阻尼项的非线性波动方程的初值问题utt-2buxxt+auxxxx=β(ux^n)x,;u(x,0)=ψ(x),ut(x,0)=ψ(x),其中b〉0,β≠0为任意实数,n≥2为整 当a≠b^2,ψ∈L1(R)∩H^2(R),ψ∈K1(R)∩L3(R)时,上述问题存在唯一的整体光滑解。 相似文献
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BOUNDEDNESS OF SOLUTIONS AND EXISTENCEOF LIMIT CYCLES FOR A NONLINEAR SYSTEMOF DIFFERENTIAL EQUATIONS 总被引:4,自引:1,他引:3
IntroductionTheautonomousplanarsystemoftheformwasfirststudiedbyLevinsonandSmithintheclassicalpaper[2]astheequivalelltsystellloftheequationofLienardtypeandlateronsomeauthorshavecontributedtotiletheoryofthissystemwithrespecttoqualitativebehaviorofsolutionsll--9].InthepresentpaperwestudyasystemOfaslightlymoregeneraltype,namely,wherethefllnctionsp(y),q(y),g(x)andh(x,y)arecontilluousforallvalueoftheirarguments,and3'resubjecttotheconditionswhichensurethattheexistenceofuniquesolutiontotheinitialvalu… 相似文献
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51. IntroductionLet fi C Re (n = 1,2) be a bounded smooth domain. Consider the following nonhomogeneous initial-boundary value problem for the unsaturated Landau-Lifshitz systems offerromagnetic spin chain with Gilbert damping constant afl > 0,where adZ is the exchange constallt, u = (u', u', u'), "o(x) is smooth and satisfies the unsaturated condition, i.e., Ilo(~)I gi constant, and in IVuol' < co, "o(x)IOn = op(x). DenoteW(x) = luo(x)I. We assume 0 < m = mane < M ~ mpxW. Throughout t… 相似文献
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Zhang Linli~ Liu Anping~ Chang Tao~ 《Annals of Differential Equations》2007,23(4):581-585
In this paper,by means of iterative analysis,the existence for periodic boun- dary value problem of first-order integro-differential differential equations are considered.Some new results are obtained. 相似文献
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In this paper, we study the problems on the existence, uniqueness and stability of almost periodic solution for a class of nonlinear system. Using fixed point theorem and Lyapunov functional, the sufficient conditions are given which guarantee the existence, uniqueness and stability of almost periodic solution for the system. 相似文献
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Yu Zanping Zhou Zheyan School of Math.and Computer Science Fujian Normal University Fuzhou ) Shen Jianhe 《Annals of Differential Equations》2007,23(3):365-372
The paper aims to obtain existence and uniqueness of the solution as well as asymptotic estimate of the solution for singularly perturbed nonlinear third- order Robin boundary value problem with a turning point.In order to achieve this aim,existence and uniqueness of the solution for third-order nonlinear Robin boundary value problem is derived first based on the upper and lower solutions method under relatively weaker conditions.In this manner,the goal of this paper is gained by applying the existence and uniqueness results mentioned above. 相似文献
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We use the Fokas method to analyze the derivative nonlinear Schrodinger (DNLS) equation iqt (x, t) = -qxx (x, t)+(rq^2)x on the interval [0, L]. Assuming that the solution q(x, t) exists, we show that it can be represented in terms of the solution of a matrix Riemann- Hilbert problem formulated in the plane of the complex spectral parameter ξ. This problem has explicit (x, t) dependence, and it has jumps across {ξ∈C|Imξ^4 = 0}. The relevant jump matrices are explicitely given in terms of the spectral functions {a(ξ), b(ξ)}, {A(ξ), B(ξ)}, and {A(ξ), B(ξ)}, which in turn are defined in terms of the initial data q0(x) = q(x, 0), the bound- ary data g0(t)= q(0, t), g1(t) = qx(0, t), and another boundary values f0(t) = q(L, t), f1(t) = qx(L, t). The spectral functions are not independent, but related by a compatibility condition, the so-called global relation. 相似文献
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In this paper, the existence and the uniqueness of the local generalized solution and the local classical solution of the Cauchy problem for the generalized BBM-Burgers equationare proved. The existence and the uniqueness of the global generalized solution and the global classical solution for the Cauchy problem of equation (1) are proved when n = 3, 2, 1. Moreover, the decay property of the solution is discussed. 相似文献
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§1.IntroductionConsiderthefolowingddimensionalVlasovPoisonsystem,d=2,3,tf+v·xf-E·vf=0,f(0,x,v)=f0(x,v),E(t,x)=c(d)∫x-y|x... 相似文献