共查询到20条相似文献，搜索用时 336 毫秒
1.
We consider the integral functional
under non-standard growth assumptions that we call p(x) type: namely, we assume that
a relevant model case being the functional
Under sharp assumptions on the continuous function p(x)>1 we prove regularity of minimizers. Energies exhibiting this growth appear in several models from mathematical physics.
Accepted July 13, 2000?Published online January 22, 2001 相似文献
2.
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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3.
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
4.
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
5.
The divergence identity for punctured domain B1(0)\ {0}
suggest a viewpoint on describing the behavior of a function uC2(B1(0)\{0}) near the origin. This is useful especially on describing the singular behavior of solutions of polyharmonic equations. In this paper we mainly show that the solution u of the equation
satisfies the identity that, letting
vi=(–)iu
provided there exist s0>0 and t0 0 such that f(x,t) c|x|–tq for 0<|x|<s0 and t t0 with n–q(n–2p) and q>1.Dedicated to Professor Shui-Nee Chow on the occasion of his 60th birthday. 相似文献
6.
We investigate the asymptotic behavior of solutions of the damped nonlinear oscillator equation
where uf(u) > 0 for u ≠ 0, a(t) ≥ 0, and α is a positive constant with 0 < α ≥ 1. The case α = 1 has been investigated by a number of other authors. Here,
it is shown that the behavior of solutions in the case of sublinear damping (0 < α < 1) is completely different from that
in the case of linear damping (α = 1). Sufficient conditions for all nonoscillatory solutions to converge to zero and sufficient
conditions for the existence of a nonoscillatory solution that does not converge to zero are given. We also give sufficient
conditions for all solutions to be nonoscillatory. Some open problems for future research are also indicated.
__________
Published in Neliniini Kolyvannya, Vol. 8, No. 2, pp. 186–200, April–June, 2005. 相似文献
7.
E. N. Barron R. R. Jensen C. Y. Wang 《Archive for Rational Mechanics and Analysis》2001,157(4):255-283
The Aronsson-Euler equation for the functional
on W
g
1, ∞(Ω, ℝ
m
, i.e., W
1, ∞ with boundary data g, is
This equation has been derived for smooth absolute minimizers, i.e., a function which minimizes F on every subdomain. We prove in this paper that for m=1, n≧ 1, or n=1, m≧ 1 an absolute minimizer of F exists in W
g
1, ∞(Ω, ℝ
m
and for m= 1, n≧ 1 any absolute minimizer of F must be a viscosity solution of the Aronsson-Euler equation.
Accepted November 13, 2000?Published online April 23, 2001 相似文献
8.
We establish efficient conditions guaranteeing that every solution of the problem
|
u￠(t) 3 l(u)(t), u(a) 3 h(u), u'(t) \geq \ell (u)(t),\quad u(a) \geq h(u), 相似文献
9.
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:
10.
We study the stationary Dirac equation
11.
Stanislaus Maier-Paape Thomas Wanner 《Archive for Rational Mechanics and Analysis》2000,151(3):187-219
This paper addresses the phenomenon of spinodal decomposition for the Cahn-Hilliard equation
12.
We consider the Cauchy problem for a strictly hyperbolic, N × N quasilinear system in one-space dimension
13.
We develop the axisymmetric Synthetic Schlieren technique to study the wake of a microscale sphere settling through a density
stratification. A video-microscope was used to magnify and image apparent displacements of a micron-sized random-dot pattern.
Due to the nature of the wake, density gradient perturbations in the horizontal greatly exceed those in the vertical, requiring
modification of previously developed axisymmetric techniques. We present results for 780 and 383 μm spheres, and describe
the limiting role of noise in the system for a 157 μm sphere. This technique can be instrumental in understanding a range
of ecological and environmental oceanic processes on the microscale.
14.
Tanja Siegmann-Hegerfeld Stefan Albensoeder Hendrik C. Kuhlmann 《Experiments in fluids》2008,45(5):781-796
Two- and three-dimensional flows in nearly cuboidal cavities are investigated experimentally. A tight cavity is formed in
the gap between two long and parallel cylinders of large radii by adding rigid top, bottom, and end walls. The cross-section
perpendicular to the axes of the cylinders is nearly rectangular with aspect ratio Γ. The axial aspect ratio Λ > 10 is large
to suppress end-wall effects. The fluid motion is driven by independent and steady rotation of the cylinders about their axes
which defines two Reynolds numbers Re
1,2. Stability boundaries of the nearly two-dimensional steady flow have been determined as functions of Re
1,2 for Γ = 0.76 and Γ = 1. Up to six different three-dimensional supercritical modes have been identified. The critical thresholds
for the onset of most of the three-dimensional modes, three of which have been observed for the first time, agree well with
corresponding linear-stability calculations. Particular attention is paid to the flow for Γ = 1 under symmetric and parallel
wall motion. In that case the basic flow consists of two mirror symmetric counter-rotating parallel vortices. They become
modulated in span-wise direction as the driving increases. Detailed LDV measurements of the supercritical three-dimensional
velocity field and the bifurcation show an excellent agreement with numerical simulations.
15.
Let E be a Banach space. We prove the instability of the trivial solution of the differential equation
16.
An iterative procedure, based on the proper orthogonal decomposition (POD), first proposed by Everson and Sirovich (J Opt
Soc Am A 12(8):1657–1664, 1995) is applied to marred particle image velocimetry (PIV) data of shallow rectangular cavity flow at Mach 0.19, 0.28, 0.38,
and 0.55. The procedure estimates the POD modes while simultaneously estimating the missing vectors in the PIV data. The results
demonstrate that the absolute difference between the repaired vectors and the original PIV data approaches the experimental
uncertainty as the number of included POD modes is increased. The estimation of the dominant POD modes is also shown to converge
by examining the subspace spanned by the POD eigenfunctions.
17.
This paper is devoted to time-global solutions of the Fisher-KPP equation in ℝ
N
:
18.
This paper reports laser-Doppler measurements of the mean flow and turbulence stresses in a swirling pipe flow. Experiments were carried out under well-controlled laboratory conditions in a refractive index-matched pipe flow facility. The results show pronounced asymmetry in mean and fluctuating quantities during the downstream decay of the swirl. Experimental data reveal that the swirl significantly modifies the anisotropy of turbulence and that it can induce explosive growth of the turbulent kinetic energy during its decay. Anisotropy invariant mapping of the turbulent stresses shows that the additional flow deformation imposed by initially strong swirling motion forces turbulence in the core region to tend towards the isotropic two-component state. When turbulence reaches this limiting state it induces rapid production of turbulent kinetic energy during the swirl decay.
19.
Consider the Cauchy problem for a strictly hyperbolic, N × N quasilinear system in one space dimension
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