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1.
In order to describe slow modulations in time and space of stable or slightly unstable spatially periodic stationary solutions
of pattern forming reaction–diffusion systems, so-called phase diffusion equations and Cahn–Hilliard equations can be derived
via multiple scaling analysis as formal approximation equations. In the case that these equations degenerate, waiting time
phenomena are well known to occur. In this paper, we prove that such waiting time phenomena can also occur approximately in
the original reaction–diffusion systems by proving estimates between the formal approximations and the exact solutions of
the original systems. 相似文献
2.
This paper considers the nonexistence of periodic solutions in a class of nonlinear uncertain systems. Based on the generalized
Kalman–Yakubovich–Popov (GKYP) lemma, linear matrix inequalities (LMIs) characterizations are derived to guarantee the nonexistence
of periodic solutions in a certain frequency range. The new LMI conditions do not involve any product of the Lyapunov matrix
and the system matrices. Based on the results, a dynamic output feedback controller is designed to ensure the nonexistence
of periodic solutions in such systems. A concrete application to the Chua circuit shows the applicability and validity of
the proposed approach.
This work was supported by the National Science Foundation of China under Grants 60404007 and 60334030. 相似文献
3.
Tai Shan YI Li Hong HUANG 《数学学报(英文版)》2007,23(8):1375-1384
The authors investigate the asymptotic behavior of solutions to a class of systems of delay differential equations. It is shown that every bounded solution of such a class of systems tends to a constant vector as t→∞. Our results improve and extend some corresponding ones already known. 相似文献
4.
Nassif Ghoussoub Abbas Moameni 《Calculus of Variations and Partial Differential Equations》2009,36(1):85-118
Selfdual variational calculus is developed further and used to address questions of existence of local and global solutions
for various parabolic semi-linear equations, and Hamiltonian systems of PDEs. This allows for the resolution of such equations
under general time boundary conditions which include the more traditional ones such as initial value problems, periodic and
anti-periodic orbits, but also yield new ones such as “periodic orbits up to an isometry” for evolution equations that may
not have periodic solutions. In the process, we introduce a method for perturbing selfdual functionals in order to induce
coercivity and compactness, without destroying the selfdual character of the system.
N. Ghoussoub was partially supported by a grant from the Natural Sciences and Engineering Research Council of Canada. A. Moameni’s
research was supported by a postdoctoral fellowship at the University of British Columbia. 相似文献
5.
This paper concerns a system of nonlinear wave equations describing the vibrations of a 3-dimensional network of elastic strings.The authors derive the equations and appropriate nodal conditions,determine equilibrium solutions,and,by using the methods of quasilinear hyperbolic systems,prove that for tree networks the natural initial,boundary value problem has classical solutions existing in neighborhoods of the "stretched" equilibrium solutions.Then the local controllability of such networks near such equilibrium configurations in a certain specified time interval is proved.Finally,it is proved that,given two different equilibrium states satisfying certain conditions,it is possible to control the network from states in a small enough neighborhood of one equilibrium to any state in a suitable neighborhood of the second equilibrium over a suffciently large time interval. 相似文献
6.
S. S. Marchenkov V. S. Fedorova 《Moscow University Computational Mathematics and Cybernetics》2009,33(4):197-201
General issues concerning solutions to the systems of functional equations of multivalued logic—the dependence of solutions
on functional constants and the possibility of constructing the systems of equations having a given unique solution or a given
set of solutions—are considered. 相似文献
7.
Nassif Ghoussoub 《Frontiers of Mathematics in China》2008,3(2):167-193
Hamiltonian systems with various time boundary conditions are formulated as absolute minima of newly devised non-negative
action functionals obtained by a generalization of Bogomolnyi’s trick of ‘dcompleting squares’. Reminiscent of the selfdual
Yang-Mills equations, they are not derived from the fact that they are critical points (i.e., from the corresponding Euler-Lagrange
equations) but from being zeroes of the corresponding non-negative Lagrangians. A general method for resolving such variational
problems is also described and applied to the construction of periodic solutions for Hamiltonian systems, but also to study
certain Lagrangian intersections.
相似文献
8.
A. V. Domrin 《Theoretical and Mathematical Physics》2008,154(2):184-200
By Uhlenbeck’s results, every harmonic map from the Riemann sphere S2 to the unitary group U(n) decomposes into a product of so-called unitons: special maps from S2 to the Grassmannians Gr
k(ℂn) ⊂ U(n) satisfying certain systems of first-order differential equations. We construct a noncommutative analogue of this
factorization, applicable to those solutions of the noncommutative unitary sigma model that are finite-dimensional perturbations
of zero-energy solutions. In particular, we prove that the energy of each such solution is an integer multiple of 8π, give examples of solutions that are not equivalent to Grassmannian solutions, and study the realization of non-Grassmannian
zero modes of the Hessian of the energy functional by directions tangent to the moduli space of solutions.
__________
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 154, No. 2, pp. 220–239, February, 2008. 相似文献
9.
E. Yu. Panov 《Journal of Mathematical Sciences》2009,156(4):644-668
We consider hyperbolic conservation laws on matrix algebras. We describe entropies of such systems and study properties of
generalized entropy solutions and strong generalized entropy solutions to the Cauchy problem. Bibliography: 15 titles.
Translated from Problemy Matematicheskogo Analiza, No. 38, December 2008, pp. 73–91. 相似文献
10.
Ya. Belopolskaya 《Journal of Mathematical Sciences》1998,92(6):4256-4272
A class of nondiagonal systems of nonlinear parabolic equations that can be reduced to a scalar parabolic equation in the
phase space of a larger dimension is described. In view of such a reduction, it is possible to state the maximum principle
for solutions to systems of nonlinear parabolic equations and derive a priori C2+α-estimates for a solution to the Cauchy problem. Bibliography: 19 titles.
Translated fromProblemy Matematicheskogo Analiza, No. 16. 1997, pp. 41–67. 相似文献
11.
Differential-algebraic equations with a higher index can beapproximated by regularization algorithms. One such possibilitywas introduced by März for linear time-varying index 2systems and extended by the author to index 3 systems. In thepresent paper, Märzs approach is generalized tononlinear semiexplicit index 2 and 3 equations. The structureof the regularized solutions and their convergence propertiesare characterized in terms of asymptotic expansions. 相似文献
12.
A variety of problems in computer science, operations research, control theory, etc., can be modeled as non-linear and non-differentiable
max–min systems. This paper introduces the global optimization into such systems. The criteria for the existence and uniqueness
of the globally optimal solutions are established using the high matrix, optimal max-only projection set and k
s
-control vector of max–min functions. It is also shown that the global optimization can be accomplished through the partial
max-only projection representation with algebraic and combinatorial features. The methods are constructive and lead to an
algorithm of finding all globally optimal solutions. 相似文献
13.
Angelo Alessandri Giorgio Gnecco Marcello Sanguineti 《Journal of Optimization Theory and Applications》2010,147(2):243-262
Rates of convergence are derived for approximate solutions to optimization problems associated with the design of state estimators
for nonlinear dynamic systems. Such problems consist in minimizing the functional given by the worst-case ratio between the
ℒ
p
-norm of the estimation error and the sum of the ℒ
p
-norms of the disturbances acting on the dynamic system. The state estimator depends on an innovation function, which is searched
for as a minimizer of the functional over a subset of a suitably-defined functional space. In general, no closed-form solutions
are available for these optimization problems. Following the approach proposed in (Optim. Theory Appl. 134:445–466, 2007), suboptimal solutions are searched for over linear combinations of basis functions containing some parameters to be optimized.
The accuracies of such suboptimal solutions are estimated in terms of the number of basis functions. The estimates hold for
families of approximators used in applications, such as splines of suitable orders. 相似文献
14.
T. Jankowski 《Journal of Optimization Theory and Applications》2010,144(1):56-68
We apply the monotone iterative method to nonlinear four-point boundary conditions for differential–algebraic systems with
causal operators. Sufficient conditions under which such problems have solutions (extremal or unique) are given. An example
illustrates the theoretical results. 相似文献
15.
V. I. Tkachenko 《Ukrainian Mathematical Journal》1998,50(3):464-469
We prove the existence of a linear homogeneous almost periodic system of differential equations that has nontrivial bounded
solutions and is such that all systems from a certain neighborhood of it have no nontrivial almost periodic solutions.
Institute of Mathematics, Ukrainian Academy of Sciences, Kiev. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50,
No. 3. pp. 409–413, March, 1998. 相似文献
16.
V. V. Kozlov 《Regular and Chaotic Dynamics》2008,13(3):141-154
The paper develops an approach to the proof of the “zeroth” law of thermodynamics. The approach is based on the analysis of
weak limits of solutions to the Liouville equation as time grows infinitely. A class of linear oscillating systems is indicated
for which the average energy becomes eventually uniformly distributed among the degrees of freedom for any initial probability
density functions. An example of such systems are sympathetic pendulums. Conditions are found for nonlinear Hamiltonian systems
with finite number of degrees of freedom to converge in a weak sense to the state where the mean energies of the interacting
subsystems are the same. Some issues related to statistical models of the thermostat are discussed.
相似文献
17.
Haiyan Wang 《Journal of Nonlinear Science》2011,21(5):747-783
Much has been studied on the spreading speed and traveling wave solutions for cooperative reaction–diffusion systems. In this
paper, we shall establish the spreading speed for a large class of non-cooperative reaction–diffusion systems and characterize
the spreading speed as the slowest speed of a family of non-constant traveling wave solutions. Our results are applied to
a partially cooperative system describing interactions between ungulates and grass. 相似文献
18.
F. A. Rihan 《Computational Mathematics and Modeling》2008,19(3):292-303
Singular perturbation problems containing a small positive parameter ε occur in many areas, including biochemical kinetics, genetics, plasma physics, and mechanical and electrical systems. A uniformly
valid, reliable interpretable approximation of such problems is required. This paper provides sufficient conditions to ensure
the exponential stability of the analytical and numerical solutions of the singularly perturbed delay differential equations
with a bounded time-lag for suf.ciently small ε > 0. The Halanay inequality is used to prove the main results of the paper. A numerical example is provided to illustrate
the methodology and clarify the need for a stiff solver for numerical solutions of these problems. 相似文献
19.
This paper is the second in a series on the structure of sets of solutions to systems of equations in a free group, projections
of such sets, and the structure of elementary sets defined over a free group. In the second paper we generalize Merzlyakov’s
theorem on the existence of a formal solution associated with a positive sentence [Me]. We first construct a formal solution
to a generalAE sentence which is known to be true over some variety, and then develop tools that enable us to analyze the collection of
all such formal solutions.
Partially supported by an Israel Academy of Sciences Fellowship. 相似文献
20.
V. S. Levchenkov 《Computational Mathematics and Modeling》2000,11(2):154-163
The explicit form of solutions of Boolean equations with one unknown is obtained. The effectiveness of the method is demonstrated
for a number of equations whose solution previously has been found only in “tabular” form. The proposed approach leads to
a method for solving systems of equations in Boolean set algebra. We use it to analyze the famous paradoxes of set theory,
such as the barber paradox and the liar paradox, as well as Russell's and Cantor's paradoxes.
Translated from Nelineinaya Dinamika i Upravlenie, pp. 119–132, 1999. 相似文献