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1.
Michael Hayes 《Archive for Rational Mechanics and Analysis》1988,100(3):265-273
Communicated by K. R. Rajagopal
For
Máirín
and
Siobhán 相似文献
2.
The maximum principle for viscosity solutions of fully nonlinear second order partial differential equations 总被引:4,自引:0,他引:4
Robert Jensen 《Archive for Rational Mechanics and Analysis》1988,101(1):1-27
We prove that viscosity solutions in W
1, of the second order, fully nonlinear, equation F(D
2
u, Du, u) = 0 are unique when (i) F is degenerate elliptic and decreasing in u or (ii) F is uniformly elliptic and nonincreasing in u. We do not assume that F is convex. The method of proof involves constructing nonlinear approximation operators which map viscosity subsolutions and supersolutions onto viscosity subsolutions and supersolutions, respectively. This method is completely different from that used in Lions [8, 9] for second order problems with F convex in D
2
u and from that used by Crandall & Lions [3] and Crandall, Evans & Lions [2] for fully nonlinear first order problems.The research reported here was supported in part by grants from the Alfred P. Sloan Foundation and the National Science Foundation. 相似文献
3.
V. Nesi 《Archive for Rational Mechanics and Analysis》1996,134(1):17-51
A recent theorem due to Astala establishes the best exponent for the area distortion of planar K-quasiconformal mappings. We use a refinement of Astala's theorem due to Eremenko and Hamilton to prove new bounds on the effective conductivity of two-dimensional composites. The bounds are valid for composites made of an arbitrary finite number n of possibly anisotropic phases in prescribed volume fractions. For n= 2 we prove the optimality of the bounds under certain additional assumptions on the G-closure parameters. 相似文献
4.
Dedicated to
James B. Serrin
on the occasion of his sixtieth birthday 相似文献
5.
Eberhard Zeidler 《Archive for Rational Mechanics and Analysis》1971,41(2):81-107
Ohne ZusammenfassungHerrn Prof. Herbert Beckert
zum 50. Geburtstag
Vorgelegt von J. Serrin 相似文献
6.
A. W. Marris 《Archive for Rational Mechanics and Analysis》1988,102(4):377-384
Dedicated to Professor
Bernard D. Coleman 相似文献
7.
C. M. Dafermos 《Archive for Rational Mechanics and Analysis》1989,107(2):127-155
In Memoriam
Ronald J. DiPerna 相似文献
8.
Martin Kummer 《Archive for Rational Mechanics and Analysis》1985,91(1):55-82
We study a particular class of perturbations of the classical Kepler Hamiltonian, first in two, then in three and finally in n dimensions. At every stage of our investigation the group theoretical nature of our constructions is fully exposed.In particular we present a new regularization of the n-dimensional Kepler problem which is based on previous constructions of Guillemin & Sternberg (see [8]). This regularization is similarily related to Moser's (see [9]) as is Kustaanheimo-Stiefel's (see [4]) in three dimensions. 相似文献
9.
Peter Werner 《Archive for Rational Mechanics and Analysis》1960,6(1):231-260
Ohne Zusammenfassung
Vorgelegt von C. Müller
Zur praktischen Berechnung von U können nach Satz 2 die numerischen Methoden zur Auflösung Fredholmscher Integralgleichungen, etwa das Verfahren von Cl. Müller [10], verwendet werden. 相似文献
10.
Giuseppe Grioli 《Archive for Rational Mechanics and Analysis》1989,105(3):191-204
Communicated by M. E. Gurtin &; C. Truesdell 相似文献
11.
Gaetano Fichera 《Archive for Rational Mechanics and Analysis》1979,70(2):101-112
Dedicata a
Clifford A. Truesdell
nel Suo 60 compleanno 相似文献
12.
Jacob Burbea 《Archive for Rational Mechanics and Analysis》1981,77(4):349-358
We derive an evolution equation for the motions of patches of vorticity (vortex). Steady state solutions of this equation that include those of Kirchhoff and Moore & Saffman are established. The m-fold symmetric, m3, hypotrochoid is an exact steady solution of this equation when rotation and strain are present. When strain is absent but rotation is present, the m-fold symmetric, m2, hypotrochoid is a perturbation solution with a dispersion relation extending that of Lamb. The case of m=2 is exact and is the Kirchhoff elliptical vortex. 相似文献
13.
LAURE SAINT-RAYMOND 《Archive for Rational Mechanics and Analysis》2003,166(1):47-80
We consider here the problem of deriving rigorously, for well-prepared initial data and without any additional assumption,
dissipative or smooth solutions of the incompressible Euler equations from renormalized solutions of the Boltzmann equation.
This completes the partial results obtained by Golse [B. Perthame and L. Desvillettes eds., Series in Applied Mathematics 4 (2000), Gauthier-Villars, Paris] and Lions & Masmoudi [Arch. Rational Mech. Anal. 158 (2001), 195–211].
(Accepted June 6, 2002) Published online December 3, 2002
Communicated by Y. BRENIER 相似文献
14.
Ohne Zusammenfassung
Vorgelegt von L. Collatz
II. Teil einer bei der Naturwissenschaftlich-Philosophischen Fakultät der Technischen Hochschule zu Braunschweig eingereichten Dissertation. Referenten: Prof. Dr. R. Iglisch und Prof. Dr. H.-J. Kanold. Auch Herrn Dr. H. Eltermann bin ich für wertvolle Ratschläge zu großem Dank verpflichtet. 相似文献
15.
Lothar Jentsch 《Archive for Rational Mechanics and Analysis》1967,24(2):141-172
Ohne Zusammenfassung
Vorgelegt von H. Beckert
Den Herren Professoren H. Beckert und R. Klötzler möchte ich an dieser Stelle für das Interesse am Entstehen dieser Arbeit herzlich danken. 相似文献
16.
This paper is dedicated to the study of viscous compressible barotropic fluids in dimension N ≧ 2. We address the question of the global existence of strong solutions for initial data close to a constant state having
critical Besov regularity. First, this article shows the recent results of Charve and Danchin (Arch Ration Mech Anal 198(1):233–271, 2010) and Chen et al. (Commun Pure Appl Math 63:1173–1224, 2010) with a new proof. Our result relies on a new a priori estimate for the velocity that we derive via the intermediary of the effective velocity, which allows us to cancel out the coupling between the density and the velocity as in Haspot (Well-posedness in critical spaces for barotropic viscous fluids, 2009). Second, we improve the results of Charve and Danchin (2010) and Chen et al. (2010) by adding as in Charve and Danchin (2010) some regularity on the initial data in low frequencies. In this case we obtain global strong solutions for a class of large
initial data which rely on the results of Hoff (Arch Rational Mech Anal 139:303–354, 1997), Hoff (Commun Pure Appl Math 55(11):1365–1407, 2002), and Hoff (J Math Fluid Mech 7(3):315–338, 2005) and those of Charve and Danchin (2010) and Chen et al. (2010). We conclude by generalizing these results for general viscosity coefficients. 相似文献
17.
We present convergence results for an adaptive algorithm to compute free energies, namely the adaptive biasing force (ABF)
method (Darve and Pohorille in J Chem Phys 115(20):9169–9183, 2001; Hénin and Chipot in J Chem Phys 121:2904, 2004). The free energy is the effective potential associated to a so-called reaction coordinate ξ(q), where q = (q
1, … , q
3N
) is the position vector of an N-particle system. Computing free energy differences remains an important challenge in molecular dynamics due to the presence
of metastable regions in the potential energy surface. The ABF method uses an on-the-fly estimate of the free energy to bias
dynamics and overcome metastability. Using entropy arguments and logarithmic Sobolev inequalities, previous results have shown
that the rate of convergence of the ABF method is limited by the metastable features of the canonical measures conditioned
to being at fixed values of ξ (Lelièvre et al. in Nonlinearity 21(6):1155–1181, 2008). In this paper, we present an improvement on the existing results in the presence of such metastabilities, which is a generic
case encountered in practice. More precisely, we study the so-called bi-channel case, where two channels along the reaction
coordinate direction exist between an initial and final state, the channels being separated from each other by a region of
very low probability. With hypotheses made on ‘channel-dependent’ conditional measures, we show on a bi-channel model, which
we introduce, that the convergence of the ABF method is, in fact, not limited by metastabilities in directions orthogonal
to ξ under two crucial assumptions: (i) exchange between the two channels is possible for some values of ξ and (ii) the free energy is a good bias in each channel. This theoretical result supports recent numerical experiments (Minoukadeh et al. in J Chem Theory Comput 6:1008–1017, 2010), where the efficiency of the ABF approach is demonstrated for such a multiple-channel situation. 相似文献
18.
John M. Russell 《Applied Scientific Research》1994,53(1-2):163-186
This paper presents a survey of undisturbed flows that take one or another of the field equations of inviscid shear flow instability theory (e.g. theRayleigh equation,Taylor-Goldstein-Haurwitz equation or theKuo equation) to a differential equation satisfied by aknown transcendental function forarbitrary complex values of the parameters. Some mean velocity profiles having this feature are well known. Thus, piecewise linear mean velocity profiles take theRayleigh equations to a constant-coefficient differential equation and the exponential mean velocity profile takes theRayleigh equation to theGauss hypergeometric equation. Less well known is the fact that a variety of mean velocity profiles take theRayleigh equation to a differential equation due toKarl
Heun. These profiles include: (i) the sinusoidal profile; (ii) the hyperbolic tangent profile (an example pointed out byMiles (1963)); (iii) the profile in the form of the square of a hyperbolic secant (theBickley jet); and, (iv) a skewed velocity profile in which each component has the form of a quadratic function of the variable exp(–z/l) (in whichz is the cross-stream coordinate andl is a length scale). In all of these cases, one or another author has previously identified aregular neutral mode solution of theRayleigh equation and has expressed that solution in the form of elementary functions. Such regular neutral modes apparently represent cases in which the solution ofHeun's equation (which is normally an infinite series) truncates to a single term. The survey concludes by noting that the parabolic mean velocity profile takes theRayleigh equation to thedifferential equation of the spheroidal wave function.Dedicated to Mårten T. Landahl on the occasion of his sixty-fifth birthday by a former apprentice as a token of his respect and gratitude. 相似文献
19.
Guy Ruddock 《Archive for Rational Mechanics and Analysis》1994,127(1):1-39
In this paper we investigate the X-interface, a microstructure observed in Indium-Thallium byBasinski &Christian [5].Ball &James [3] have shown howsimple martensitic microstructures can be represented by sequences of elastic deformations which minimise a free-energy functional. In contrast we show that the X-interfacecannot be represented by such a sequence. In an attempt to understand this result we develop a less restrictive theory based onEricksen's ideas about low-energy modes of deformation for martensitic materials. This theory has some interesting conclusions for the X-interface and Indium-Thallium, for the wedge-like microstructures analysed recently byBhattacharya [6], and for the general problem of microstructures which cannot be represented by minimising sequences. The calculations in this paper apply only to cubic-to-tetragonal transformations. 相似文献
20.
Winfried Eckart 《Continuum Mechanics and Thermodynamics》2000,12(5):341-362
In this paper we propose a phenomenological theory for electrorheological fluids. In general these are suspensions which undergo dramatic changes in their material properties if they are exposed to an electric
field. In the context of continuum mechanics these fluids can be modeled as non-Newtonian fluids. Recalling the governing equations of rational thermodynamics and electrodynamics of moving media (Maxwell-Minkowski-equations), we derive suitable governing equations of electrorheology using essentially two assumptions concerning magnetic
quantities. Furthermore we introduce a 3-dimensional nonlinear constitutive equation for the Cauchy stress tensor which is an extension of the model proposed by Ružička (see [14]). Assuming a viscometric flow, we compare the shear stress of our model with other well known models and fit the parameters by using measurements that
were obtained in a rotational viscometer. Excellent agreement between model and measurements is achieved. On the basis of
these results we propose a 3-dimensional model, the so-called extended
Casson
-model. This model is investigated further for a channel flow configuration with a homogeneous electric field. We determine analytical solutions for the electric field, the velocity and the volumetric flow rate and illustrate the velocity
profiles and the predicted pressure drop. The velocity profiles are flattened compared to parabolic profiles and become more
flat if the electric field increases.
Received March 21, 2000 相似文献