Stability and controllability of the electromagneto-elastic system.
Stability and convergence of an effective numerical method for the time-space fractional Fokker-Planck equation with a nonlinear source term.
Stability and convergence of two discrete schemes for a degenerate solutal non-isothermal phase-field model
We analyze two numerical schemes of Euler type in time and C0 finite-element type with -approximation in space for solving a phase-field model of a binary alloy with thermal properties. This model is written as a highly non-linear parabolic system with three unknowns: phase-field, solute concentration and temperature, where the diffusion for the temperature and solute concentration may degenerate. The first scheme is nonlinear, unconditionally stable and convergent. The other scheme is linear...
Stability and error estimates valid for infinite time, for strongly monotone and infinitely stiff evolution equations
Stability and gradient dynamical systems.
The objective in these notes is to present an approach to dynamical systems in infinite dimensions. It does not seem reasonable to make a comparison of all of the orbits of the dynamics of two systems on non locally compact infinite dimensional spaces. Therefore, we choose to compare them on the set of globally defined bounded solutions. Fundamental problems are posed and several important results are stated when this set is compact. We then give results on the dynamical system which will ensure...
Stability and instability of equilibria on singular domains
We show existence of nonconstant stable equilibria for the Neumann reaction-diffusion problem on domains with fractures inside. We also show that the stability properties of all hyperbolic equilibria remain unchanged under domain perturbation in a quite general sense, covered by the theory of Mosco convergence.
Stability and Instability of Solitary Wave Solutions of a Nonlinear Dispersive System of Benjamin-Bona-Mahony Type
2000 Mathematics Subject Classification: 35B35, 35B40, 35Q35, 76B25, 76E30.This paper concerns the orbital stability and instability of solitary waves of the system of coupling equations of Benjamin-Bona-Mahony type. By applying the abstract results of Grillakis, Shatah and Strauss and detailed spectral analysis, we obtain the existence and stability of the solitary waves.Partially Supported by Grant MM-810/98 of MESC and by Scientefic Research Grant 19/12.03.2003 of Shumen University.
Stability and saddle-point property for a linear autonomous functional parabolic equation
Stability and semiclassics in self-generated fields
We consider non-interacting particles subject to a fixed external potential and a self-generated magnetic field . The total energy includes the field energy and we minimize over all particle states and magnetic fields. In the case of spin-1/2 particles this minimization leads to the coupled Maxwell-Pauli system. The parameter tunes the coupling strength between the field and the particles and it effectively determines the strength of the field. We investigate the stability and the semiclassical...
Stability criteria for a class of discrete reaction-diffusion equations.
Stability estimate for strong solutions of the Navier-Stokes system and its applications.
Stability estimates for a linearized Muskat problem
Stability estimates for an inverse problem for the linear Boltzmann equation.
In this paper we consider the inverse problem of recovering the total extinction coefficient and the collision kernel for the time-dependent Boltzmann equation via boundary measurements. We obtain stability estimates for the extinction coefficient in terms of the albedo operator and also an identification result for the collision kernel.
Stability estimates of an inverse problem for the stationary transport equation
Stability for a certain class of numerical methods – abstract approach and application to the stationary Navier-Stokes equations
We consider some abstract nonlinear equations in a separable Hilbert space and some class of approximate equations on closed linear subspaces of . The main result concerns stability with respect to the approximation of the space . We prove that, generically, the set of all solutions of the exact equation is the limit in the sense of the Hausdorff metric over of the sets of approximate solutions, over some filterbase on the family of all closed linear subspaces of . The abstract results are...
Stability for a coupled system of wave equations of Kirchhoff type with nonlocal boundary conditions.
Stability for a diffusive delayed predator-prey model with modified Leslie-Gower and Holling-type II schemes
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
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
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 -maximal regularity
We study stability and integrability of linear non-autonomous evolutionary Cauchy-problem where is a bounded and strongly measurable function and , are Banach spaces such that . Our main concern is to characterize -maximal regularity and to give an explicit approximation of the problem (P).