共查询到20条相似文献,搜索用时 484 毫秒
1.
赵雅明 《纯粹数学与应用数学》1997,13(2):99-103
在正交增量的随机积分基础上,利用Lipschitz条件,讨论了下面一类两参数随机积分方程解的唯一性。X(s,t)=Z(s,0)+Z(0,t)-Z(0,0)+∫Rstα(u,v,X)dMuv+∫Rstβ(u,v,X)dmuv+∫R^stγ1(u,v,u',v',X)dMuvdMu'v'+∫R^2stγ2(u,v,u',v',X)dMuvdmu'v'+∫R^2stγ3(u,v,u',v',X)dmuv 相似文献
2.
Inanagestructuredpopulationmodel,thefishessystemofafishgroundcanbedescribedasfollowingmodel:u(a,t)t+u(a,t)a=-μ(a)u(a,t), 0aA,t0,u(a,0)=u0(a),u(0,t)=f[E(t)]E(t),E(t)=∫A0b(a)u(a,t)da.(1)Whereu(a,t)denotesagedistributivedensityfunctionoffishedatt… 相似文献
3.
Runge-Kutta方法关于时滞奇异摄动问题的误差分析 总被引:2,自引:0,他引:2
1.引言 用(,)表示Euclidean空间的内积,||·||为相应范数,考虑时滞奇异摄动问题(SPPDs)这里。∈,r(r>0)是常数, 和 是给定的函数,f: 和 是给定的充分光滑的映射,它们满足下面的条件这里w1和-w2是具有适度大小的常数且 分别关于其它变量满足 Lipschitz 条件.不失一般性,假设w2=1(参见[1]) 与经典 Lipschitz条件相比,条件(1.2a)更弱.事实上,当(1.3)中的 L具有适度大小时,就能… 相似文献
4.
Shi Guoliang 《数学季刊》1998,(3)
§1. IntroductionTheexistencefortheboundaryvalueproblemshavebeenwidelystudiedrecently.Inthispaper,wewilldiscusstheBVPofthefollowingconditions:u(n)+a(t)f(u)=0,0<t<1,u(k)(0)=0,0kn-2(1.1)u(1)=0, where(h1)a:(0,1)→(0,∞)isacontinuousfunction.(h2)f:[0,∞)→[… 相似文献
5.
1.引言方程是在国内外引起广泛关注的一类重要的非线性发展方程.文[1]在函数f(s)满足局部 Lip-schitz条件及单调性条件(f(s2)-f(s1))(s2-s1)> 0的假设下得到了(1.1)初边值问题整体弱解的存在与唯一性;文[2]用 Galerkin方法,研究了(1.1)的初边值问题,周期边值问题和初值问题,并在函数f’(s)下方有界的假设下得到了整体强解的存在与唯一性. 本文在有限区域 QT=[0,1]×[0,T](T> 0)上讨论方程(1.1)带有初值条件和边值条件(u(x,t)为未知… 相似文献
6.
§1. IntroductionIn[1,2],AronsonandWeinbergerhavestudiedsystematiclythescalarnonlineardiffu-sionequationinonespacevariableut=uxx+φ(u),(1.1)whereu=u(x,t)andφ(u)isanonlinearfunction.Equation(1.1)arisesinseveralapplica-tions;See[1,2]and[3]forinformationa… 相似文献
7.
§1. IntroductionandResultInthisarticleweareconcernedwiththedecayofglobalsolutionoftheinitial-boundaryvalueproblemforthefollowingnonlinearhyperbolicequationutt+Au+|ut|αut=f(x,t) inΩ×R+,(1)u(x,0)=u0(x),ut(x,0)=u1(x) x∈Ω,(2)u(x,t)=0 (x,t… 相似文献
8.
本文考虑下面的Dirichlet问题利用粘性解理论证明了;当H,Г满足一定条件时,(DP)的粘性解u(x,t)满足:如果ψ∈Ca,a/2,则u(x,t)∈Ca,a/2,若ψ=0,则u(x,t)是Lipschitz连续的. 相似文献
9.
§1. IntroductionRecently,thesemilinearellipticequations△u+f(u)=0(1.1)u(x)→0as|x|→∞(1.2)inRnwereconsideredwidely(see[1]-[7]).Inthenicepapers[1]and[2],itwasprovedthatanypositivesolutionof(1.1)mustberadialincasef(u)∈C1+δ(δ>0).Therefore,anypositivesoluti… 相似文献
10.
Lu Guofu 《高校应用数学学报(英文版)》1999,14(1):30-44
§1IntroductionInthepaper,weconsidertheinitialandboundaryvalueproblemasfolows:ut=Δ(gradφ(u))+αΔb(u)+f(x,t,u),(x,t)∈QT=Ω×(0,T](... 相似文献
11.
<正> 本文研究二阶半线性椭圆边值问题■的多重解(符号详见§3),其中φ(x,t)允许对t是不连续的.一些自由边界问题可以化归这类问题.为了统一处理φ(x,t)对t连续与不连续两种情形,我们采用集值映射的观点.为此推广了经典的算子与Hammerstein算子到集值映射,并发展了集值映射的Leray-Schauder度理论;与已有的集值映射理论不同,现在处理的是映射串(定 相似文献
12.
This paper is concerned with a equation, which is a model of filtration in partially saturated porous media, with mixed boundary condition of Dirichlet-Neumann type {∂_tb(u) - ∇ • a [∇u + k(b(u))] = f \qquad in \quad (0, ∞) × Ω u = h(t, x) \qquad on \quad (0, ∞) × Γ_0 v • a [∇u + k(b(u))] = g(t, x) \qquad on \quad (0, ∞) × Γ_1 We have proved that there exists one and only one periodic solution of the problem under the data f, g and h with same period. Moreover, we have proved that the unique periodic solution ω is asymptotically statble in the sense that for any solution u of the problem b(u(t)) - b(ω(t)) → 0\qquad in L²(Ω) as t → ∞. 相似文献
13.
Gao Feng Zheng 《数学学报(英文版)》2012,28(7):1491-1506
It is shown that any solution to the semilinear problem{ ut = uxx + δ(1-u)-p , (x, t) ∈ (-1 , 1) × (0 , T ), u( ±1 , t) = 0, t ∈ (0 , T ), u(x, 0) = u0(x) 1, x ∈ [ 1 , 1] either touches 1 in finite time or converges smoothly to a steady state as t →∞. Some extensions of this result to higher dimensions are also discussed. 相似文献
14.
S. G. Pyatkov 《Journal of Mathematical Sciences》2008,150(5):2422-2433
In the paper, we study the inverse problem of finding the solution u and the coefficient q from the following data:
where G ⊂ ℝn is a bounded domain with boundary Γ and L is a second-order elliptic operator. We prove that the problem is locally solvable in time or in the case where the norms
of its data are sufficiently small.
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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 12, No. 4, pp. 187–202, 2006. 相似文献
15.
Cauchy Problem for Semilinear Wave Equations in Four Space Dimensions with Small Initial Data 下载免费PDF全文
Yi Zhou 《偏微分方程(英文版)》1995,8(2):135-144
In this paper, we consider the Cauchy problem ◻u(t,x) = |u(t,x)|^p, (t,x) ∈ R^+ × R^4 t = 0 : u = φ(x), u_t = ψ(x), x ∈ R^4 where ◻ = ∂²_t - Σ^4_{i=1}∂²_x_i, is the wave operator, φ, ψ ∈ C^∞_0 (R^4). We prove that for p > 2 the problem has a global solution provided tile initial data is sufficiently small. 相似文献
16.
刘衍胜 《应用泛函分析学报》2004,6(3):193-199
考虑下述奇异半线性反应扩散方程初值问题(()-1-t△u=ut+f(x),t>0,x∈RN
lim u(t,x)=0,x∈RN t→0=)其中r>0,△=∑( )/( )x2i,f(x)非负且f(x)∈L∞(RN).首先利用增算子不动点定理,重新证明了IVP在(0,+∞)上至少存在一个非负解,并给出了IVP解的迭代逼近序列.其次获得了一个有关IVP(1)正解的无限增长性的结果.最后,证明了当r>1时,去掉条件1/r-1≥n/2,IVP的正解u(t)同样会产生爆破.研究结果表明情形limut→+∞(t,x)=+∞不会出现. 相似文献
17.
关于Fujita型反应扩散方程组的Cauchy问题 总被引:5,自引:1,他引:5
本文研究Fujita型反应扩散方程组ut-Δu=α1|u|q1-1u+β1|v|p1-1v,(x∈RN,t>0),vt-Δv=α2|u|q2-1u+β2|v|p2-1v,u(x,0)=u0(x)0,v(x,0)=v0(x)0,(x∈RN)Lp解的整体存在性和有限时间Blow up问题.这里qi>1,pi>1(i=1,2),α10,α2>0,β1>0,β20,1p+∞. 相似文献
18.
设E是具弱序列连续对偶映像自反Banach空间, C是E中闭凸集, T:C→ C是具非空不动点集F(T)的非扩张映像.给定u∈ C,对任意初值x0∈ C,实数列{αn}n∞=0,{βn}∞n=0∈ (0,1),满足如下条件:(i)sum from n=α to ∞α_n=∞, α_n→0;(ii)β_n∈[0,α) for some α∈(0,1);(iii)sun for n=α to ∞|α_(n-1) α_n|<∞,sum from n=α|β_(n-1)-β_n|<∞设{x_n}_(n_1)~∞是由下式定义的迭代序列:{y_n=β_nx_n (1-β_n)Tx_n x_(n 1)=α_nu (1-α_n)y_n Then {x_n}_(n=1)~∞则{x_n}_(n=1)~∞强收敛于T的某不动点. 相似文献
19.
变系数Euler-Bernoulli梁振动发展系统的存在性 总被引:1,自引:0,他引:1
讨论变系数Euler-Bernoulli梁振动系统{uu(x,t) η(t)uxxxx(x,t)=0,0<x<1,0≤t≤T u(0,t)=ux(0,t)=0,0≤t≤t -uxxx(1,t) muu(1,t)=-αu1(1,t) βuxxx(1,t),0≤t≤T uxt(1,t) =-γuxx(1,t),0≤t≤t u(x,0)=u1(x),u1(x,0),0≤x≤1证明了该系统产生一个发展系统. 相似文献
20.
Chunlai Mu 《偏微分方程(英文版)》1995,8(4):341-350
We consider L^p-L^q estimates for the solution u(t,x) to tbe following perturbed Klein-Gordon equation ∂_{tt}u - Δu + u + V(x)u = 0 \qquad x∈ R^n, n ≥ 3 u(x,0) = 0, ∂_tu(x,0) = f(x) We assume that the potential V(x) and the initial data f(x) are compact, and V(x) is sufficiently small, then the solution u(t,x) of the above problem satisfies ||u(t)||_q ≤ Ct^{-a}||f||_p for t > 1 where a is the piecewise-linear function of 1/p and 1/q. 相似文献