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1.
We give sufficient conditions for the extendability of solutions of a nonlinear difference equation “to the left” in a Banach
space.
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Translated from Neliniini Kolyvannya, Vol. 10, No. 3, pp. 298–302, July–September, 2007. 相似文献
2.
In this article, we study the large time behavior of solutions of first-order Hamilton–Jacobi Equations set in a bounded domain
with nonlinear Neumann boundary conditions, including the case of dynamical boundary conditions. We establish general convergence
results for viscosity solutions of these Cauchy–Neumann problems by using two fairly different methods: the first one relies
only on partial differential equations methods, which provides results even when the Hamiltonians are not convex, and the
second one is an optimal control/dynamical system approach, named the “weak KAM approach”, which requires the convexity of
Hamiltonians and gives formulas for asymptotic solutions based on Aubry–Mather sets. 相似文献
3.
N. I. Blashchak 《Nonlinear Oscillations》2005,8(2):152-156
We obtain sufficient conditions for the existence of periodic solutions of a system of nonlinear functional partial differential
equations.
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Translated from Neliniini Kolyvannya, Vol. 8, No. 2, pp. 154–158, April–June, 2005. 相似文献
4.
A.V. Vel’hach 《Nonlinear Oscillations》2009,12(1):19-26
We establish sufficient conditions for systems of nonlinear functional differential equations of neutral type to have solutions
that are continuously differentiable and bounded for t ∈ ℝ (together with their first derivatives) and investigate the asymptotic properties of these solutions.
Translated from Neliniini Kolyvannya, Vol. 12, No. 1, pp. 20–26, January–March, 2009. 相似文献
5.
For a weakly nonlinear differential equation in a Banach space, we establish necessary and sufficient conditions for the existence
of solutions bounded on the entire real axis under the assumption that the generating equation has bounded solutions and the
corresponding homogeneous equation admits an exponential dichotomy on the semiaxes.
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Translated from Neliniini Kolyvannya, Vol. 11, No. 2, pp. 151–159, April–June, 2008. 相似文献
6.
We consider the problem of the existence of solutions of an optimal-control problem for a nonlinear elliptic equation with
Dirichlet conditions on the boundary in the case where the control functions are the coefficients in the principal part of
the differential operator. It is shown that this problem has an optimal solutions in the class of generalized solenoidal matrices.
Translated from Neliniini Kolyvannya, Vol. 12, No. 1, pp. 59–72, January–March, 2009. 相似文献
7.
A constitutive equation for polymer solutions and melts is obtained on the basis of the dynamics of noninteracting dumbbells
moving in a nonlinear anisotropic fluid. The equation obtained is used to describe nonlinear effects under conditions of simple
shear and steady-state flow in a circular tube and for the numerical investigation of a flow in a finite cylinder with a rotating
end face.
Barnaul. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 3–13, January–February,
2000. 相似文献
8.
We consider the Navier–Stokes equations in a thin domain of which the top and bottom surfaces are not flat. The velocity fields
are subject to the Navier conditions on those boundaries and the periodicity condition on the other sides of the domain. This
toy model arises from studies of climate and oceanic flows. We show that the strong solutions exist for all time provided
the initial data belong to a “large” set in the Sobolev space H
1. Furthermore we show, for both the autonomous and the nonautonomous problems, the existence of a global attractor for the
class of all strong solutions. This attractor is proved to be also the global attractor for the Leray–Hopf weak solutions
of the Navier–Stokes equations. One issue that arises here is a nontrivial contribution due to the boundary terms. We show
how the boundary conditions imposed on the velocity fields affect the estimates of the Stokes operator and the (nonlinear)
inertial term in the Navier–Stokes equations. This results in a new estimate of the trilinear term, which in turn permits
a short and simple proof of the existence of strong solutions for all time. 相似文献
9.
N. A. Bohai 《Nonlinear Oscillations》2007,10(2):169-175
We obtain sufficient conditions for the existence and uniqueness of continuous N-periodic solutions (N is a positive integer number) for a certain class of systems of nonlinear difference equations with continuous argument and
study their properties.
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Translated from Neliniini Kolyvannya, Vol. 10, No. 2, pp. 177–183, April–June, 2007. 相似文献
10.
Stephan Blazy Sergueï Nazarov Maria Specovius-Neugebauer 《Journal of Mathematical Fluid Mechanics》2007,9(1):1-33
In a three-dimensional domain Ω with J cylindrical outlets to infinity the problem is treated how solutions to the stationary Stokes and Navier–Stokes system with
pressure conditions at infinity can be approximated by solutions on bounded subdomains. The optimal artificial boundary conditions
turn out to have singular coefficients. Existence, uniqueness and asymptotically precise estimates for the truncation error
are proved for the linear problem and for the nonlinear problem with small data. The results include also estimates for the
so called “do-nothing” condition. 相似文献
11.
Mergen H. Ghayesh Siavash Kazemirad Mohammad A. Darabi Pamela Woo 《Archive of Applied Mechanics (Ingenieur Archiv)》2012,82(3):317-331
Thermo-mechanical vibrations of a simply supported spring-mass-beam system are investigated analytically in this paper. Taking
into account the thermal effects, the nonlinear equations of motion and internal/external boundary conditions are derived
through Hamilton’s principle and constitutive relations. Under quasi-static assumptions, the equations governing the longitudinal
motion are transformed into functions of transverse displacements, which results in three integro-partial differential equations
with coupling terms. These are solved using the direct multiple-scale method, leading to closed-form solutions for the mode
functions, nonlinear natural frequencies and frequency–response curves of the system. The influence of system parameters on
the linear and nonlinear natural frequencies, mode functions, and frequency–response curves is studied through numerical parametric
analysis. It is shown that the vibration characteristics depend on the mid-plane stretching, intra-span spring, point mass,
and temperature change. 相似文献
12.
C. W. Lim S. K. Lai B. S. Wu W. P. Sun Y. Yang C. Wang 《Archive of Applied Mechanics (Ingenieur Archiv)》2009,79(5):411-431
An analytical approach is developed for the nonlinear oscillation of a conservative, two-degree-of-freedom (TDOF) mass-spring
system with serial combined linear–nonlinear stiffness excited by a constant external force. The main idea of the proposed
approach lies in two categories, the first one is the transformation of two nonlinear differential equations of a two-mass
system using suitable intermediate variables into a single nonlinear differential equation. Another is the treatment a quadratic
nonlinear oscillator (QNO) by the modified Lindstedt–Poincaré (L-P) method presented recently by the authors. The first-order
and second-order analytical approximations for the modified L-P method are established for the QNOs with satisfactory results.
After solving the nonlinear differential equation, the displacements of two-mass system can be obtained directly from the
governing linear second-order differential equation. Unlike the common perturbation method, the modified L-P method is valid
for weak as well as strong nonlinear oscillation systems. On the other hand, the new approach yields simple approximate analytical
expressions valid for small as well as large amplitudes of oscillation. In short, this new approach yields extended scope
of applicability, simplicity, flexibility in application, and avoidance of complicated numerical integration as compared to
the previous approaches such as the perturbation and classical harmonic balance methods. Two examples of nonlinear TDOF mass-spring
systems excited by a constant external force are selected and the approximate solutions are verified with the exact solutions
derived from the Jacobi elliptic function and also the numerical fourth-order Runge–Kutta solutions. 相似文献
13.
P. Balakumar 《Theoretical and Computational Fluid Dynamics》1997,9(2):103-119
Two-dimensional nonlinear equilibrium solutions for the plane Poiseuille–Couette flow are computed by directly solving the
full Navier–Stokes equations as a nonlinear eigenvalue problem. The equations are solved using the two-point fourth-order
compact scheme and the Newton–Raphson iteration technique. The linear eigenvalue computations show that the combined Poiseuille–Couette
flow is stable at all Reynolds numbers when the Couette velocity component σ2 exceeds 0.34552. Starting with the neutral solution for the plane Poiseuille flow, the nonlinear neutral surfaces for the
combined Poiseuille–Couette flow were mapped out by gradually increasing the velocity component σ2. It is found that, for small σ2, the neutral surfaces stay in the same family as that for the plane Poiseuille flow, and the nonlinear critical Reynolds
number gradually increases with increasing σ2. When the Couette velocity component is increased further, the neutral curve deviates from that for the Poiseuille flow with
an appearance of a new loop at low wave numbers and at very low energy. By gradually increasing the σ2 values at a constant Reynolds number, the nonlinear critical Reynolds numbers were determined as a function of σ2. The results show that the nonlinear neutral curve is similar in shape to a linear case. The critical Reynolds number increases
slowly up to σ2∼ 0.2 and remains constant until σ2∼ 0.58. Beyond σ2 > 0.59, the critical Reynolds number increases sharply. From the computed results it is concluded that two-dimensional nonlinear
equilibrium solutions do not exist beyond a critical σ2 value of about 0.59.
Received: 26 November 1996 and accepted 12 May 1997 相似文献
14.
João Paulo Dias Mário Figueira Hermano Frid 《Archive for Rational Mechanics and Analysis》2010,196(3):981-1010
Motivated by Benney’s general theory, we propose new models for short wave–long wave interactions when the long waves are
described by nonlinear systems of conservation laws. We prove the strong convergence of the solutions of the vanishing viscosity
and short wave–long wave interactions systems by using compactness results from compensated compactness theory and new energy
estimates obtained for the coupled systems. We analyze several of the representative examples, such as scalar conservation
laws, general symmetric systems, nonlinear elasticity and nonlinear electromagnetism. 相似文献
15.
M. A. Abdou 《Nonlinear dynamics》2008,52(1-2):1-9
In this paper, the Exp-function method with the aid of the symbolic computational system Maple is used to obtain the generalized
solitonary solutions and periodic solutions for nonlinear evolution equations arising in mathematical physics, namely, (2+1)-dimensional
Konopelchenko–Dubrovsky equations, the (3+1)-dimensional Jimbo–Miwa equation, the Kadomtsev–Petviashvili (KP) equation, and
the (2+1)-dimensional sine-Gordon equation. It is shown that the Exp-function method, with the help of symbolic computation,
provides a powerful mathematical tool for solving other nonlinear evolution equations arising in mathematical physics. 相似文献
16.
Giuseppe Alì Vidar Furuholt Roberto Natalini Isabella Torcicollo 《Transport in Porous Media》2007,69(2):175-188
We present a numerical investigation of a degenerate nonlinear parabolic–elliptic system, which describes the chemical aggression
of limestones under the attack of SO2, in high permeability regime. This system has been introduced in the first part of this paper. We present a finite element
scheme for our model and its numerical stability is given under suitable CFL conditions. Numerical tests are discussed as
well as some examples of the numerical behavior of the solutions. 相似文献
17.
Boyan Sirakov 《Archive for Rational Mechanics and Analysis》2010,195(2):579-607
We get existence, uniqueness and non-uniqueness of viscosity solutions of uniformly elliptic fully nonlinear equations of
the Hamilton–Jacobi–Bellman–Isaacs type with unbounded ingredients and quadratic growth in the gradient without hypotheses
of convexity or properness. Some of our results are new even for equations in divergence form. 相似文献
18.
V. D. Bondar’ 《Journal of Applied Mechanics and Technical Physics》2009,50(2):352-359
The plane strain of an incompressible body is studied with geometrical and physical nonlinearity and potential forces taken
into account. A nonlinear system of equations for strains is obtained in actual variables, and conditions of its ellipticity
are derived in terms of the elastic potential. Boundary conditions for strains are found from specified loads. Analytical
solutions of the boundary problem in strains and their corresponding stress fields are found for the case of identical elongations.
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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 2, pp. 217–225, March–April, 2009 相似文献
19.
Giuseppe Alì Vidar Furuholt Roberto Natalini Isabella Torcicollo 《Transport in Porous Media》2007,69(1):109-122
We introduce a degenerate nonlinear parabolic–elliptic system, which describes the chemical aggression of limestones under
the attack of SO2, in high permeability regime. By means of a dimensional scaling, the qualitative behavior of the solutions in the fast reaction
limit is investigated. Explicit asymptotic conditions for the front formation are derived. 相似文献
20.
We prove the existence of Cantor families of periodic solutions for nonlinear wave equations in higher spatial dimensions
with periodic boundary conditions. We study both forced and autonomous PDEs. In the latter case our theorems generalize previous
results of Bourgain to more general nonlinearities of class C
k
and assuming weaker non-resonance conditions. Our solutions have Sobolev regularity both in time and space. The proofs are
based on a differentiable Nash–Moser iteration scheme, where it is sufficient to get estimates of interpolation-type for the
inverse linearized operators. Our approach works also in presence of very large “clusters of small divisors”. 相似文献