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The Cahn-Hilliard variational inequality is a non-standard parabolic variational inequality of fourth order for which straightforward numerical approaches cannot be applied. We propose a primal-dual active set method which can be interpreted as a semi-smooth Newton method as solution technique for the discretized Cahn-Hilliard variational inequality. A (semi-)implicit Euler discretization is used in time and a piecewise linear finite element discretization of splitting type is used in space leading...
The Cahn-Hilliard variational inequality is a non-standard
parabolic variational inequality of fourth order for which
straightforward numerical
approaches cannot be applied. We propose a primal-dual active set
method which can be interpreted as a semi-smooth Newton method as
solution technique for the discretized Cahn-Hilliard variational
inequality. A (semi-)implicit Euler discretization is used in time
and a piecewise linear finite element discretization of splitting
type is used in space...
An existence and uniqueness theorem for a nonlinear parabolic system of partial differential equations, connected with the theory of heat conduction with a transition phase in a concentrated capacity, is given in sufficiently general hypotheses on the data.
In this paper we study the linear thermodynamical problem of mixtures of thermoelastic solids. We use some results of the semigroup theory to obtain an existence theorem for the initial value problem with homogeneous Dirichlet boundary conditions. Continuous dependence of solutions upon the initial data and body forces is also established. We finish with a study of the asymptotic behavior of solutions of the homogeneous problem.
We present in this work a numerical study of a problem governed by Navier-Stokes
equations and heat equation. The mathematical problem under consideration is obtained by
modelling the natural convection of an incompressible fluid, in laminar flow between two
horizontal concentric coaxial cylinders, the temperature of the inner cylinder is supposed
to be greater than the outer one. The numerical simulation of the flow is carried out by
collocation-Legendre...
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...
The paper deals with the Field-Körös-Noyes' model of the Belousov-Yhabotinskij reaction. By means of the method of the Ljapunov function a sufficient condition is determined that the non-trivial critical point of this model be asymptotically stable with respect to a certain set.
Steady-state system of equations for incompressible, possibly non-Newtonean of the -power type, viscous flow coupled with the heat equation is considered in a smooth bounded domain , or 3, with heat sources allowed to have a natural -structure and even to be measures. The existence of a distributional solution is shown by a fixed-point technique for sufficiently small data if (for ) or if (for ).
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