共查询到20条相似文献,搜索用时 15 毫秒
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A. M. Izosimov 《Moscow University Mathematics Bulletin》2013,68(1):80-82
It is well known that rotations of a free three-dimensional rigid body around the long and short axes of inertia are stable, while the rotation around the intermediate axis is unstable. We generalize this result to the case of a rigid body in a space of arbitrary dimension. 相似文献
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In this paper results are obtained concerning the number of positive stationary solutions in simple models of the Calvin cycle of photosynthesis and the stability of these solutions. It is proved that there are open sets of parameters in the model of Zhu et al. (2009) for which there exist two positive stationary solutions. There are never more than two isolated positive stationary solutions but under certain explicit special conditions on the parameters there is a whole continuum of positive stationary solutions. It is also shown that in the set of parameter values for which two isolated positive stationary solutions exist there is an open subset where one of the solutions is asymptotically stable and the other is unstable. In related models derived from the work of Grimbs et al. (2011), for which it was known that more than one positive stationary solution exists, it is proved that there are parameter values for which one of these solutions is asymptotically stable and the other unstable. A key technical aspect of the proofs is to exploit the fact that there is a bifurcation where the centre manifold is one-dimensional. 相似文献
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A. G. Khachatryan 《Journal of Mathematical Sciences》1983,21(3):451-464
One investigates the problem of the stability of the solutions of nonlinear parabolic initial-boundary-value problems relative to small perturbations of the class C with any0 under suitable restrictions (depending on ) on the structure of the nonlinear terms.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akad. Nauk SSSR, Vol. 84, pp. 286–304, 1979.The author expresses his thanks to his scientific advisor, V. A. Solonnikov, for his help in the completion of this paper. 相似文献
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Ryuji Kajikiya 《Journal of Differential Equations》2018,264(2):786-834
In the present paper, we study the initial boundary value problem of the sublinear parabolic equation. We prove the existence of solutions and investigate the stability and instability of stationary solutions. We show that a unique positive and a unique negative stationary solutions are exponentially stable and give the exact exponent. We prove that small stationary solutions are unstable. For one space dimensional autonomous equations, we elucidate the structure of stationary solutions and study the stability of all stationary solutions. 相似文献
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We study the large-time behaviour of a non-local evolution equation for the density of particles or individuals subject to an external and an interaction potential. In particular, we consider interaction potentials which are singular in the sense that their first derivative is discontinuous at the origin.For locally attractive singular interaction potentials we prove under a linear stability condition local non-linear stability of stationary states consisting of a finite sum of Dirac masses. For singular repulsive interaction potentials we show the stability of stationary states of uniformly bounded solutions under a convexity condition.Finally, we present numerical simulations to illustrate our results. 相似文献
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P. Amster C.G. Averbuj M.C. Mariani 《Journal of Mathematical Analysis and Applications》2002,276(1):231-238
We study by topological methods a nonlinear differential equation generalizing the Black-Scholes formula for an option pricing model with stochastic volatility. We prove the existence of at least a solution of the stationary Dirichlet problem applying an upper and lower solutions method. Moreover, we construct a solution by an iterative procedure. 相似文献
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Kenjiro Maginu 《Journal of Mathematical Analysis and Applications》1978,63(1):224-243
We consider a parabolic partial differential equation ut = uxx + f(u) on a compact interval of spatial variable x with Dirichlet boundary conditions. The stability of stationary solutions of this system is studied by the use of Liapunov's second method. We obtain necessary and sufficient conditions for the stability, asymptotic stability, neutral stability, instability, and conditional stability. These conditions are closely connected with the conditions for the existence of the stationary solutions. 相似文献
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M. S. Ginovian 《Probability Theory and Related Fields》1994,100(3):395-406
Summary A central limit theorem for Toeplitz type quadratic functionals of a stationary Gaussian processX(t),t, is proved, generalizing the result of Avram [1] for discrete time processes. The result is applied to the problem of nonparametric estimation of linear functionals of an unknown spectral density function. We give some upper bounds for the minimax mean square risk of the nonparametric estimators, similar to those by Ibragimov and Has'minskii [12] for a probability density function. 相似文献
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Mitsuo Higaki 《Mathematische Nachrichten》2023,296(1):314-338
We investigate the stability of an exact stationary flow in an exterior cylinder. The horizontal velocity is the two-dimensional rotating flow in an exterior disk with a critical spatial decay, for which the L2 stability is known under smallness conditions. We prove its stability property for three-dimensional perturbations although the Hardy type inequalities are absent as in the two-dimensional case. The proof uses a large time estimate for the linearized equations exhibiting different behaviors in the Fourier modes, namely, the standard L2- decay of the two-dimensional mode and an exponential decay of the three-dimensional modes. 相似文献
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Due to the ongoing miniaturization of devices quantum effects are no longer negligible in semiconductor modeling. Also temperature effects play a role for example when identifying hot spots in devices. QET models, which can be derived via moment method from the Wigner-BKG model, include both physical features. We analyze the stability of stationary states. Suitable numerical methods and computational results are presented. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
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T. A. Burton 《Annali di Matematica Pura ed Applicata》1973,95(1):193-209
Summary In this paper we consider a system of two first order differential equations {x′=P(x,y). y′=Q(x,y)}. We usually assume that
∂P/∂x+∂Q/∂y vanish identically in a certain region. A number of conditions are then given to insure boundedness of solutions or asymptotic
stability of the zero solution.
Entrata in Redazione il 5 gennaio 1972. 相似文献
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Kelly Black 《Numerical Methods for Partial Differential Equations》1993,9(4):395-409
A method is examined to approximate the interface conditions for Chebyshev polynomial approximations to the solutions of parabolic problems, and a smoothing technique is used to calculate the interface conditions for a domain decomposition method. The methods uses a polynomial of one less degree then the full approximation to calculate the first derivative so that interface values can be calculated by using only the adjacent subdomains. Theoretical results are given for the consistency of the scheme and practical results are presented. Computational results are given for both a fourth-order Runga-Kutta methods and an explicit/implicit scheme. © 1993 John Wiley & Sons, Inc. 相似文献
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We study stability properties of a class of piecewise affine systems of ordinary differential equations arising in the modeling of gene regulatory networks. Our method goes back to the concept of a Filippov stationary solution (in the narrow sense) to a differential inclusion corresponding to the system in question. The main result of the paper justifies a reduction principle in the stability analysis enabling to omit the variables that are not singular, i.e. that stay away from the discontinuity set of the system. We suggest also “the first approximation method” to study asymptotic stability of stationary solutions based on calculating the principal part of the system, which is 0-homogeneous rather than linear. This leads to an efficient algorithm of how to check asymptotic stability without calculating the eigenvalues of the system?s Jacobian. In Appendix A we discuss and compare two other concepts of stationary solutions to the system in question. 相似文献
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Paul Deuring 《Applications of Mathematics》2007,52(1):59-94
We consider numerical approximations of stationary incompressible Navier-Stokes flows in 3D exterior domains, with nonzero
velocity at infinity. It is shown that a P1-P1 stabilized finite element method proposed by C. Rebollo: A term by term stabilization
algorithm for finite element solution of incompressible flow problems, Numer. Math. 79 (1998), 283–319, is stable when applied
to a Navier-Stokes flow in a truncated exterior domain with a pointwise boundary condition on the artificial boundary. 相似文献
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In this paper we discuss the asymptotic stability of stationary solutions for the non-isentropic Euler-Maxwell system in R3. It is known in the authors’ previous works [17, 18, 19] that the Euler-Maxwell system verifies the decay property of the regularity-loss type. In this paper we first prove the existence and uniqueness of a small stationary solution. Then we show that the non-stationary problemhas a global solution in a neighborhood of the stationary solution under smallness condition on the initial perturbation. Moreover, we show the asymptotic convergence of the solution toward the stationary solution as time tends to infinity. The crucial point of the proof is to derive a priori estimates by using the energy method. 相似文献
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We study control problems for the stationary magnetohydrodynamic equations. In these problems, one has to find an unknown
vector function occurring in the boundary condition for the magnetic field and the solution of the boundary value problem
in question by minimizing a performance functional depending on the velocity and pressure. We derive new a priori estimates
for the solutions of the original boundary value problem and the extremal problem and prove theorems on the local uniqueness
and stability of solutions for specific performance functionals. 相似文献
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We study extremal problems of boundary control for stationary heat convection equations with Dirichlet boundary conditions
on velocity and temperature. As the cost functional we choose the mean square integral deviation of the required temperature
field from a given temperature field measured in some part of the flow region. The controls are functions appearing in the
Dirichlet conditions on velocity and temperature. We prove the stability of solutions to these problems with respect to certain
perturbations of both the quality functional and one of the known functions appearing in the original equations of the model. 相似文献