共查询到20条相似文献，搜索用时 62 毫秒
1.
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.
In this paper we consider the equation
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3.
In this paper, the solution of a 2-D weak singular integral equation of the first kind
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4.
Let E be a Banach space. We prove the instability of the trivial solution of the differential equation where f: [0, +∞) × E → ℝ is a continuous mapping for which
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Translated from Neliniini Kolyvannya, Vol. 8, No. 3, pp. 404–414, July–September, 2005. 相似文献
5.
Let u, p be a weak solution of the stationary Navier-Stokes equations in a bounded domain N, 5N . If u, p satisfy the additional conditions |
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6.
In order to capture the complexities of two-phase flow in heterogeneous porous media, we have used the method of large-scale averaging and spatially periodic models of the local heterogeneities. The analysis leads to the large-scale form of the momentum equations for the two immiscible fluids, a theoretical representation for the large-scale permeability tensor, and a dynamic, large-scale capillary pressure. The prediction of the permeability tensor and the dynamic capillary pressure requires the solution of a large-scale closure problem. In our initial study (Quintard and Whitaker, 1988), the solution to the closure problem was restricted to the quasi-steady condition and small spatial gradients. In this work, we have relaxed the constraint of small spatial gradients and developed a dynamic solution to the closure problem that takes into account some, but not all, of the transient effects that occur at the closure level. The analysis leads to continuity and momentum equations for the -phase that are given by |
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7.
We establish a general weak* lower semicontinuity result in the space BD(Ω) of functions of bounded deformation for functionals
of the form
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$ {ll} \,\mathcal{F}(u) := &\int_\Omega f (x, \mathcal{E} u) \;{\rm d} x + \int_\Omega f^\infty \left( x, \frac{{\rm d} E^s u}{{\rm d} |{E^s u}|} \right) \;{\rm d} |{E^s u}| \\ &+ \int_{\partial \Omega} f^\infty \left( x, u|_{\partial \Omega} \odot n_\Omega \right) \;{\rm d} \mathcal{H}^{d-1}, \qquad u \in {\rm BD}(\Omega). $ \begin{array}{ll} \,\mathcal{F}(u) := &\int_\Omega f (x, \mathcal{E} u) \;{\rm d} x + \int_\Omega f^\infty \left( x, \frac{{\rm d} E^s u}{{\rm d} |{E^s u}|} \right) \;{\rm d} |{E^s u}| \\ &+ \int_{\partial \Omega} f^\infty \left( x, u|_{\partial \Omega} \odot n_\Omega \right) \;{\rm d} \mathcal{H}^{d-1}, \qquad u \in {\rm BD}(\Omega). \end{array} 相似文献
8.
We study the limit of the hyperbolic–parabolic approximation
The function is defined in such a way as to guarantee that the initial boundary value problem is well posed even if is not invertible. The data and are constant. When is invertible, the previous problem takes the simpler form Again, the data and are constant. The conservative case is included in the previous formulations. Convergence of the , smallness of the total variation and other technical hypotheses are assumed, and a complete characterization of the limit
is provided. The most interesting points are the following: First, the boundary characteristic case is considered, that is,
one eigenvalue of can be 0. Second, as pointed out before, we take into account the possibility that is not invertible. To deal with this case, we take as hypotheses conditions that were introduced by Kawashima and Shizuta
relying on physically meaningful examples. We also introduce a new condition of block linear degeneracy. We prove that, if
this condition is not satisfied, then pathological behaviors may occur. 相似文献
9.
The following nonlinear hyperbolic equation is discussed in this paper: where The model comes from the transverse deflection equation of an extensible beam. We prove that there exists a unique local solution of the above equation as M depends on x. 相似文献
10.
In this paper, we consider the following PDE involving two Sobolev–Hardy critical exponents,
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$ \label{0.1}\left\{\begin{aligned}& \Delta u + \lambda\frac{u^{2^*(s_1)-1}}{|x|^{s_1}} + \frac{u^{2^*(s_2)-1}}{|x|^{s_2}} =0 \quad \rm {in}\,\,\Omega,\quad\quad\quad(0.1)\\ & u=0 \quad {\rm on }\,\,\Omega, \end{aligned} \right.$ \label{0.1}\left\{\begin{aligned}& \Delta u + \lambda\frac{u^{2^*(s_1)-1}}{|x|^{s_1}} + \frac{u^{2^*(s_2)-1}}{|x|^{s_2}} =0 \quad \rm {in}\,\,\Omega,\quad\quad\quad(0.1)\\ & u=0 \quad {\rm on }\,\,\Omega, \end{aligned} \right. 相似文献
11.
Ｃｏｎｓｉｄｅｒｉｎｇｔｈｅｈｉｇｈｅｒｄｉｍｅｎｓｉｏｎａｌｐｅｒｉｏｄｉｃｓｙｓｔｅｍｓｗｉｔｈｄｅｌａｙｏｆｔｈｅｆｏｒｍｘ′（ｔ）＝Ａ（ｔ,ｘ（ｔ））ｘ（ｔ）＋ｆ（ｔ,ｘ（ｔ－τ））,（１）ｘ′（ｔ）＝ｇｒａｄＧ（ｘ（ｔ））＋ｆ（ｔ,ｘ（ｔ－... 相似文献
12.
A new forced convection parameter |
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14.
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
15.
The system of ordinary differential equations |
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16.
ＩｎｔｒｏｄｕｃｔｉｏｎＡｔｐｒｅｓｅｎｔ,ｔｈｅｒｅａｒｅｏｎｌｙａｆｅｗｐａｐｅｒｓ［１～３］ｈａｖｉｎｇｂｅｎｐｕｂｌｉｓｈｅｄｏｎｔｈｅｇｌｏｂａｌｅｘｉｓｔｅｎｃｅｏｆｐｅｒｉｏｄｉｃｓｏｌｕｔｉｏｎｓｆｏｒｎｅｕｔｒａｌｄｅｌａｙｐｏｐｕ... 相似文献
17.
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 {a n}
n=0
∞
, {β n}
n=0
∞
be two real sequences in (0, 1) satisfying: ; Assume that {u n}
n=0
∞
and {υ n}
n=0
∞
are two sequences in X satisfying ‖u n‖ = 0(α n) and ‖υ n‖ → 0 as n → ∞. For arbitrary x 0 ε X, the iteration sequence {x n} is defined by Moreover, suppose that {Sx n} and {Sy n} are bounded, then {x n} converges strongly to the unique fixed point of S. 相似文献
18.
１ＰｒｏｂｌｅｍｓａｎｄＭａｉｎＲｅｓｕｌｔｓＩｎｔｈｉｓｐａｐｅｒ,ｗｅｓｔｕｄｙｔｈｅｎｏｎｌｉｎｅａｒｖｉｂｒａｔｉｏｎｓｏｆｉｎｆｉｎｉｔｅｒｏｄｓｗｉｔｈｖｉｓｃｏｅｌａｓｔｉｃｉｔｙ．Ｔｈｅｃｏｎｓｔｉｔｕｔｉｏｎｌａｗｏｆｔｈｅｒｏｄｓ... 相似文献
19.
The thermal decomposition of CS 2 highly diluted in Ar was studied behind reflected shock waves by monitoring time-dependent absorption profiles of S( 3P) and S( 1D) using atomic resonance absorption spectroscopy (ARAS). The rate coefficient of the reaction: |
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20.
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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