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Displaying 1061 – 1080 of 1688

Stability for a certain class of numerical methods – abstract approach and application to the stationary Navier-Stokes equations

Elżbieta Motyl (2012)

Annales de la faculté des sciences de Toulouse Mathématiques

We consider some abstract nonlinear equations in a separable Hilbert space $H$ and some class of approximate equations on closed linear subspaces of $H$ . The main result concerns stability with respect to the approximation of the space $H$ . We prove that, generically, the set of all solutions of the exact equation is the limit in the sense of the Hausdorff metric over $H$ of the sets of approximate solutions, over some filterbase on the family of all closed linear subspaces of $H$ . The abstract results are...

Stability for a coupled system of wave equations of Kirchhoff type with nonlocal boundary conditions.

Ferreira, Jorge, Pereira, Ducival C., Santos, Mauro L. (2003)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Stability for a diffusive delayed predator-prey model with modified Leslie-Gower and Holling-type II schemes

Yanling Tian (2014)

Applications of Mathematics

A diffusive delayed predator-prey model with modified Leslie-Gower and Holling-type II schemes is considered. Local stability for each constant steady state is studied by analyzing the eigenvalues. Some simple and easily verifiable sufficient conditions for global stability are obtained by virtue of the stability of the related FDE and some monotonous iterative sequences. Numerical simulations and reasonable biological explanations are carried out to illustrate the main results and the justification...

Stability for approximation methods of the one-dimensional Kobayashi-Warren-Carter system

Hiroshi Watanabe, Ken Shirakawa (2014)

Mathematica Bohemica

A one-dimensional version of a gradient system, known as “Kobayashi-Warren-Carter system”, is considered. In view of the difficulty of the uniqueness, we here set our goal to ensure a “stability” which comes out in the approximation approaches to the solutions. Based on this, the Main Theorem concludes that there is an admissible range of approximation differences, and in the scope of this range, any approximation method leads to a uniform type of solutions having a certain common features. Further,...

Stability for dissipative magneto-elastic systems

Reinhard Racke (2003)

Banach Center Publications

In this survey we first recall results on the asymptotic behavior of solutions in classical thermoelasticity. Then we report on recent results in linear magneto-thermo-elasticity and magneto-elasticity, respectively.

Stability for non-autonomous linear evolution equations with $L^{p}$ -maximal regularity

Hafida Laasri, Omar El-Mennaoui (2013)

Czechoslovak Mathematical Journal

We study stability and integrability of linear non-autonomous evolutionary Cauchy-problem $(P) \{\begin{matrix} \dot{u} (t) + A (t) u (t) = f (t) t -a.e. on [0, τ], u (0) = 0, \end{matrix}$ where $A : [0, τ] \to ℒ (X, D)$ is a bounded and strongly measurable function and $X$ , $D$ are Banach spaces such that $D \underset{d}{\to} ↪ X$ . Our main concern is to characterize $L^{p}$ -maximal regularity and to give an explicit approximation of the problem (P).

Stability for semilinear parabolic equations with decaying potentials in Rn and dynamical approach to the existence of ground states

Philippe Souplet, Qi S. Zhang (2002)

Annales de l'I.H.P. Analyse non linéaire

Stability in nonlinear evolution problems by means of fixed point theorems

Jaromír J. Koliha, Ivan Straškraba (1997)

Commentationes Mathematicae Universitatis Carolinae

The stabilization of solutions to an abstract differential equation is investigated. The initial value problem is considered in the form of an integral equation. The equation is solved by means of the Banach contraction mapping theorem or the Schauder fixed point theorem in the space of functions decreasing to zero at an appropriate rate. Stable manifolds for singular perturbation problems are compared with each other. A possible application is illustrated on an initial-boundary-value problem for...

Stability in Obstacle Problems.

O. Martio, Li Gongbao (1994)

Mathematica Scandinavica

Stability in the energy space for chains of solitons of the one-dimensional Gross-Pitaevskii equation

Fabrice Béthuel, Philippe Gravejat, Didier Smets (2014)

Annales de l’institut Fourier

We establish the stability in the energy space for sums of solitons of the one-dimensional Gross-Pitaevskii equation when their speeds are mutually distinct and distinct from zero, and when the solitons are initially well-separated and spatially ordered according to their speeds.

Stability of a family of multi-time-level difference schemes for the advection equation.

Rolf Jeltsch, Peywand Kiani (1991/1992)

Numerische Mathematik

Stability of a finite element method for 3D exterior stationary Navier-Stokes flows

Paul Deuring (2007)

Applications of Mathematics

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....

Stability of a numerical method for solving the 3 D inverse scattering problem with fixed energy data.

A.G. Ramm (1991)

Journal für die reine und angewandte Mathematik

Stability of a second order of accuracy difference scheme for hyperbolic equation in a Hilbert space.

Ashyralyev, Allaberen, Koksal, Mehmet Emir (2007)

Discrete Dynamics in Nature and Society

Stability of classes of mappings and Hölder continuity of higher derivatives of elliptic solutions to systems of nonlinear differential equations.

Kopylov, A. P. (2002)

Sibirskij Matematicheskij Zhurnal

Stability of Constant Solutions to the Navier-Stokes System in ℝ³

Piotr Bogusław Mucha (2001)

Applicationes Mathematicae

The paper examines the initial value problem for the Navier-Stokes system of viscous incompressible fluids in the three-dimensional space. We prove stability of regular solutions which tend to constant flows sufficiently fast. We show that a perturbation of a regular solution is bounded in $W_{r}^{2, 1} (ℝ ³ \times [k, k + 1])$ for k ∈ ℕ. The result is obtained under the assumption of smallness of the L₂-norm of the perturbing initial data. We do not assume smallness of the $W_{r}^{2 - 2 / r} (ℝ ³)$ -norm of the perturbing initial data or smallness of the...

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