共查询到20条相似文献，搜索用时 15 毫秒
1.
Iterative solution of nonlinear equations with strongly accretive operators in Banach spaces 总被引：1，自引：0，他引：1
周海云 《应用数学和力学(英文版)》1999,20(3):282-289
1IntroductionandPreliminariesLetXbearealBanachspacewithnormIJ'11andadualX'.ThenormalizeddualitymappingJ:X~ZxisdefinedbyJx={x'eX*I(x,x')=11x112=11x if'},where',')denotesthegeneralizeddualitypairing.Itiswell-knownthatifX isstrictlyconvex,Jissingle-valuedandJ(tx)=tjxforallt201xeX.IfX*isuniformlyconvex,thenJisuniformlycontinuousonanyboundedsubsetSofX(of.Browde,fljandBarbuL2]).AnoperatorTwithdomainD(T)andrangeR(T)inXissaidtobeaccretiveifforeveryx,y6D(T),thereexistsajeJ(x--y)suchthat(T… 相似文献
2.
Let X be a uniformly smooth real Banach space. Let T:X → X be continuos and strongly accretive operator. For a given f ε X,
define S: X → X by Sx =f−Tx+x, for all x ε X. Let {an}
n=0
∞
, {βn}
n=0
∞
be two real sequences in (0, 1) satisfying:
;
Assume that {un}
n=0
∞
and {υn}
n=0
∞
are two sequences in X satisfying ‖un‖ = 0(αn) and ‖υn‖ → 0 as n → ∞. For arbitrary x0 ε X, the iteration sequence {xn} is defined by
Moreover, suppose that {Sxn} and {Syn} are bounded, then {xn} converges strongly to the unique fixed point of S. 相似文献
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3.
王培光 《应用数学和力学(英文版)》1999,20(6):698-704
ＩｎｔｒｏｄｕｃｔｉｏｎＯｗｉｎｇｔｏｔｈｅｅｘｔｅｎｓｉｖｅａｐｐｌｉｃａｔｉｏｎｏｆｎｅｕｔｒａｌｅｑｕａｔｉｏｎｓ,ｍｏｒｅａｎｄｍｏｒｅｓｔｕｄｉｅｓｈａｖｅｂｅｎｍａｄｅｏｎｔｈｅｂｅｈａｖｉｏｒｏｆｔｈｅｓｏｌｕｔｉｏｎｓ［１,２］．Ｆｏ... 相似文献
4.
Stability of a class of neural network models with delay 总被引：6，自引：0，他引：6
ＩｎｔｒｏｄｕｃｔｉｏｎＲｅｃｅｎｔｌｙ,ｔｈｅｏｒｅｔｉｃａｌａｎｄａｐｌｉｅｄｓｔｕｄｉｅｓｏｆｎｅｕｒａｌｎｅｔｗｏｒｋｍｏｄｅｌｈａｖｅｂｅｎｔｈｅｎｅｗｆｏｃｕｓｏｆｓｔｕｄｉｅｓｉｎｔｈｅｗｏｒｌｄ．Ｉｔｉｓｗｅｌ＿ｋｎｏｗｎｔｈａｔｑｕ... 相似文献
5.
In this paper, first a class of fractional differential equations are obtained by using the fractional variational principles.
We find a fractional Lagrangian L(x(t), where
a
c
D
t
α
x(t)) and 0<α<1, such that the following is the corresponding Euler–Lagrange
At last, exact solutions for some Euler–Lagrange equations are presented. In particular, we consider the following equations
where g(t) and f(t) are suitable functions.
D. Baleanu is on leave of absence from Institute of Space Sciences, P.O. BOX MG-23, 76900 Magurele-Bucharest, Romania. e-mail:
baleanu@venus.nipne.ro. 相似文献
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| (2) |
| (3) |
6.
ITERATIVE PROCESS TO -HEMICONTRACTIVE OPERATOR AND-STRONGLY ACCRETIVE OPERATOR EQUATIONS 总被引：1，自引：0，他引：1
ＩｎｔｒｏｄｕｃｔｉｏｎＬｅｔＥｂｅａｎａｒｂｉｔｒａｒｙＢａｎａｃｈｓｐａｃｅ ,Ｅ ｂｅｉｔｓｄｕａｌｓｐａｃｅａｎｄ〈ｘ ,ｆ 〉ｂｅｔｈｅｇｅｎｅｒａｌｉｚｅｄｄｕａｌｉｔｙｐａｉｒｉｎｇｂｅｔｗｅｅｎｘ∈Ｅａｎｄｆ ∈Ｅ .ＴｈｅｍａｐｐｉｎｇＪ :Ｅ→ 2 Ｅ ｄｅｆｉｎｅｄｂｙＪ(ｘ) =ｆ ∈Ｅ :〈ｘ ,ｆ 〉 =‖ｆ ‖‖ｘ‖ ,‖ｆ ‖ =‖ｘ‖ｉｓｃａｌｌｅｄｔｈｅｎｏｒｍａｌｉｚｅｄｄｕａｌｉｔｙｍａｐｐｉｎｇ .ＩｆＥ ｉｓｓｔｒｉｃｔｌｙｃｏｎｖｅｘ ,ｔｈｅｎＪｉｓｓｉｎｇｌｅ＿ｖａｌｕｅｄ .Ｗｅｓｈ… 相似文献
7.
K. Pileckas 《Journal of Mathematical Fluid Mechanics》2006,8(4):542-563
The existence and uniqueness of a solution to the nonstationary Navier–Stokes system having a prescribed flux in an infinite
cylinder is proved. We assume that the initial data and the external forces do not depend on x3 and find the solution (u, p) having the following form
where x′ = (x1, x2). Such solution generalize the nonstationary Poiseuille solutions. 相似文献
8.
This paper deals with connected branches of nonstationary periodic trajectories of Hamilton equations
emanating from the degenerate stationary point
for H being the generalized Hénon-Heiles (HH) Hamiltonian:
or the generalized Yang-Mills (YM) Hamiltonian:
The existence of such branches has been proved. Minimal periods of searched trajectories near x0 have been described. 相似文献
9.
郭艾 《应用数学和力学(英文版)》1999,20(6):683-689
１ＰｒｏｂｌｅｍｓａｎｄＭａｉｎＲｅｓｕｌｔｓＩｎｔｈｉｓｐａｐｅｒ,ｗｅｓｔｕｄｙｔｈｅｎｏｎｌｉｎｅａｒｖｉｂｒａｔｉｏｎｓｏｆｉｎｆｉｎｉｔｅｒｏｄｓｗｉｔｈｖｉｓｃｏｅｌａｓｔｉｃｉｔｙ．Ｔｈｅｃｏｎｓｔｉｔｕｔｉｏｎｌａｗｏｆｔｈｅｒｏｄｓ... 相似文献
10.
In association with multi-inhomogeneity problems, a special class of eigenstrains is discovered to give rise to disturbance
stresses of interesting nature. Some previously unnoticed properties of Eshelby’s tensors prove useful in this accomplishment.
Consider the set of nested similar ellipsoidal domains {Ω1, Ω2,⋯,Ω
N+1}, which are embedded in an infinite isotropic medium. Suppose that
in which and ξ
t
a
p
, p=1,2,3 are the principal half axes of Ω
t
. Suppose, the distribution of eigenstrain, ε
ij
*(x) over the regions Γ
t
=Ω
t+1−Ω
t
, t=1,2,⋯,N can be expressed as
where x
k
x
l
⋯x
m
is of order n, and f
ijkl ⋯m
(t) represents 3N(n+2)(n+1) different piecewise continuous functions whose arguments are ∑
p=1
3
x
p
2 /a
p
2. The nature of the disturbance stresses due to various classes of the piecewise nonuniform distribution of eigenstrains,
obtained via superpositions of Eq. (‡) is predicted and an infinite number of impotent eigenstrains are introduced. The present theory not only provides a general
framework for handling a broad range of nonuniform distribution of eigenstrains exactly, but also has great implications in
employing the equivalent inclusion method (EIM) to study the behavior of composites with functionally graded reinforcements.
The paper is dedicated to professor Toshio Mura. 相似文献
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11.
Xinyu He 《Journal of Mathematical Fluid Mechanics》2007,9(3):398-410
Let
be the exterior of the closed unit ball. Consider the self-similar Euler system
Setting α = β = 1/2 gives the limiting case of Leray’s self-similar Navier–Stokes equations. Assuming smoothness and smallness of the boundary
data on ∂Ω, we prove that this system has a unique solution
, vanishing at infinity, precisely
The self-similarity transformation is v(x, t) = u(y)/(t* − t)α, y = x/(t* − t)β, where v(x, t) is a solution to the Euler equations. The existence of smooth function u(y) implies that the solution v(x, t) blows up at (x*, t*), x* = 0, t* < + ∞. This isolated singularity has bounded energy with unbounded L
2 − norm of curl v. 相似文献
12.
This paper studies exact analytical solutions in closed form of the difference equation
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相似文献
13.
Let E be a Banach space. We prove the instability of the trivial solution of the differential equation
14.
朱勇 《应用数学和力学(英文版)》1998,19(11):1059-1063
I.IntroductionItiswell-knobal.nthatKorteweg-deVriesequationisacanonicalmodeltodescribethebalanceofthenonlineareffectandthedispersiveeffectofaphysicalsystem.Thisequationpossessestheso-called'soliton"solution,whichhasbeenfoundnumericallybyZabuskyandKruskall'].Ho-c'Jlever,sometimesthebalanceofnonlinearityanddispersionofasystemmayleadtoa,integroditTerentialequationinsteadofadifferentialequation.Forinstance,inthestudyofvortexbreakdownofanunboundedrotatingfluidLeibovich12]derivedfollowingnonline… 相似文献
15.
李永昆 《应用数学和力学(英文版)》2000,21(7):849-854
ＩｎｔｒｏｄｕｃｔｉｏｎＣｏｎｓｉｄｅｒｔｈｅｎｏｎｌｉｎｅａｒａｕｔｏｎｏｍｏｕｓｄｅｌａｙｄｉｆｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎｘ′(ｔ) ∑ｍｉ=1ｐｉｆｉ(ｘ(ｔ-τｉ) ) =0 (1 )ａｎｄｔｈｅｌｉｎｅａｒｅｑｕａｔｉｏｎｘ′(ｔ) ∑ｍｉ=1ｐｉｘ(ｔ-τｉ) =0 ,(2 )ｗｈｅｒｅ ,ｐｉ ∈ (0 ,∞ ) ,τｉ ∈ [0 ,∞ )ａｎｄｆｉ ∈Ｃ(Ｒ ,Ｒ)ｆｏｒｉ =1 ,… ,ｍ .ＩｎＲｅｆ.[1 ] ,ｔｈｅｌｉｎｅａｒｉｚｅｄｏｓｃｉｌｌａｔｉｏｎｓｏｆＥｑ .(1 )ｗａｓｓｔｕｄｉｅｄａｎｄｉｔｗａｓｐｒｏｖｅｄｔｈａｔｉｆｔ… 相似文献
16.
17.
It is well-known that a KAM torus can be considered as a graph of smooth viscosity solution. Salamon and Zehnder (Comment
Math Helv 64:84–132, 1989) have proved that there exist invariant tori having prescribed Diophantine frequencies for nearly
integrable and positively definite Lagrangian systems with associated Hamiltonian H, whose Diophantine index is τ. If the invariant torus is represented as in the cotangent bundle , then we can show that for any viscosity solution u (x, P), which satisfies the H-J Eq. (1.1),
18.
We study the dynamics and regularity of level sets in solutions of the semilinear parabolic equation
19.
黄先开 《应用数学和力学(英文版)》1999,20(10):1116-1120
ＩｎｔｒｏｄｕｃｔｉｏｎＩｎｔｈｅｒｅｃｅｎｔｙｅａｒｓ,ｗｉｔｈａｌｏｔｏｆａｐｐｌｉｃａｔｉｏｎｓｏｆｎｅｕｒａｌｎｅｔｗｏｒｋｍｏｄｅｌｓ,ｍａｎｙａｕｔｈｏｒｓ［１～３］ａｒｅｉｎｔｅｒｅｓｔｅｄｉｎｔｈｅｒｅｓｅａｒｃｈｏｆｔｈｅｓｔｒｕｃｔｕｒｅａｎｄｐｅｒｆｏｒｍａｎｃｅｆｏｒｔｈｅｓｅｎｅｔｗｏｒｋｓ．ＢｅｃａｕｓｅＨｏｐｆｉｅｌｄｎｅｕｒａｌｎｅｔｗｏｒｋｗｅｌｌｓｉｍｕｌａｔｅｔｈｅｅｃｏｌｏｇｉｃａｌｓｙｓｔｅｍ,ｍａｎｙｓｔｕｄｉｅｓａｒｅｃｏｎｃｅｎｔｒａｔｅｄｏｎｔｈ… 相似文献
20.
李永昆 《应用数学和力学(英文版)》1999,20(5):579-584
ＩｎｔｒｏｄｕｃｔｉｏｎＡｔｐｒｅｓｅｎｔ,ｔｈｅｒｅａｒｅｏｎｌｙａｆｅｗｐａｐｅｒｓ［１～３］ｈａｖｉｎｇｂｅｎｐｕｂｌｉｓｈｅｄｏｎｔｈｅｇｌｏｂａｌｅｘｉｓｔｅｎｃｅｏｆｐｅｒｉｏｄｉｃｓｏｌｕｔｉｏｎｓｆｏｒｎｅｕｔｒａｌｄｅｌａｙｐｏｐｕ... 相似文献
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