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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 and convergence of two discrete schemes for a degenerate solutal non-isothermal phase-field model

Francisco Guillén-González, Juan Vicente Gutiérrez-Santacreu (2009)

ESAIM: Mathematical Modelling and Numerical Analysis

We analyze two numerical schemes of Euler type in time and C0 finite-element type with 1 -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 gradient dynamical systems.

Jack K. Hale (2004)

Revista Matemática Complutense

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

Maria Gokieli, Nicolas Varchon (2009)

Banach Center Publications

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

Hakkaev, Sevdzhan (2003)

Serdica Mathematical Journal

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 semiclassics in self-generated fields

László Erdős, Soren Fournais, Jan Philip Solovej (2013)

Journal of the European Mathematical Society

We consider non-interacting particles subject to a fixed external potential V and a self-generated magnetic field B . The total energy includes the field energy β B 2 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 β 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 estimates for an inverse problem for the linear Boltzmann equation.

Rolci Cipolatti, Carlos M. Motta, Nilson C. Roberty (2006)

Revista Matemática Complutense

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.

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