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Stability analysis of phase boundary motion by surface diffusion with triple junction

Harald Garcke, Kazuo Ito, Yoshihito Kohsaka (2009)

Banach Center Publications

The linearized stability of stationary solutions for the surface diffusion flow with a triple junction is studied. We derive the second variation of the energy functional under the constraint that the enclosed areas are preserved and show a linearized stability criterion with the help of the H - 1 -gradient flow structure of the evolution problem and the analysis of eigenvalues of a corresponding differential operator.

Stability and consistency of the semi-implicit co-volume scheme for regularized mean curvature flow equation in level set formulation

Angela Handlovičová, Karol Mikula (2008)

Applications of Mathematics

We show stability and consistency of the linear semi-implicit complementary volume numerical scheme for solving the regularized, in the sense of Evans and Spruck, mean curvature flow equation in the level set formulation. The numerical method is based on the finite volume methodology using the so-called complementary volumes to a finite element triangulation. The scheme gives the solution in an efficient and unconditionally stable way.

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 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 × [ 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...

Stability of hydrodynamic model for semiconductor

Massimiliano Daniele Rosini (2005)

Archivum Mathematicum

In this paper we study the stability of transonic strong shock solutions of the steady state one-dimensional unipolar hydrodynamic model for semiconductors in the isentropic case. The approach is based on the construction of a pseudo-local symmetrizer and on the paradifferential calculus with parameters, which combines the work of Bony-Meyer and the introduction of a large parameter.

Stability of oscillating boundary layers in rotating fluids

Nader Masmoudi, Frédéric Rousset (2008)

Annales scientifiques de l'École Normale Supérieure

We prove the linear and non-linear stability of oscillating Ekman boundary layers for rotating fluids in the so-called ill-prepared case under a spectral hypothesis. Here, we deal with the case where the viscosity and the Rossby number are both equal to ε . This study generalizes the study of [23] where a smallness condition was imposed and the study of [26] where the well-prepared case was treated.

Stability of periodic stationary solutions of scalar conservation laws with space-periodic flux

Anne-Laure Dalibard (2011)

Journal of the European Mathematical Society

This article investigates the long-time behaviour of parabolic scalar conservation laws of the type ∂ t u + div y A ( y , u ) - Δ y u = 0 , where y ∈ ℝ N and the flux A is periodic in y . More specifically, we consider the case when the initial data is an L 1 disturbance of a stationary periodic solution. We show, under polynomial growth assumptions on the flux, that the difference between u and the stationary solution behaves in L 1 norm like a self-similar profile for large times. The proof uses a time and space change of variables which is...

Currently displaying 301 – 320 of 462