On a phase-field model with a logarithmic nonlinearity

Alain Miranville

Displaying similar documents to “On a phase-field model with a logarithmic nonlinearity”

On the Caginalp system with dynamic boundary conditions and singular potentials

Laurence Cherfils, Alain Miranville (2009)

Applications of Mathematics

Similarity:

This article is devoted to the study of the Caginalp phase field system with dynamic boundary conditions and singular potentials. We first show that, for initial data in $H^{2}$ , the solutions are strictly separated from the singularities of the potential. This turns out to be our main argument in the proof of the existence and uniqueness of solutions. We then prove the existence of global attractors. In the last part of the article, we adapt well-known results concerning the Łojasiewicz inequality...

A semidiscretization scheme for a phase-field type model for solidification.

Vaz, Cristina, Boldrini, José Luiz (2006)

Portugaliae Mathematica. Nova Série

Similarity:

Existence for the stationary MHD-equations coupled to heat transfer with nonlocal radiation effects

Pierre-Étienne Druet (2009)

Czechoslovak Mathematical Journal

Similarity:

We consider the problem of influencing the motion of an electrically conducting fluid with an applied steady magnetic field. Since the flow is originating from buoyancy, heat transfer has to be included in the model. The stationary system of magnetohydrodynamics is considered, and an approximation of Boussinesq type is used to describe the buoyancy. The heat sources given by the dissipation of current and the viscous friction are not neglected in the fluid. The vessel containing the...

Global solution to a generalized nonisothermal Ginzburg-Landau system

Nesrine Fterich (2010)

Applications of Mathematics

Similarity:

The article deals with a nonlinear generalized Ginzburg-Landau (Allen-Cahn) system of PDEs accounting for nonisothermal phase transition phenomena which was recently derived by A. Miranville and G. Schimperna: Nonisothermal phase separation based on a microforce balance, Discrete Contin. Dyn. Syst., Ser. B, (2005), 753–768. The existence of solutions to a related Neumann-Robin problem is established in an $N \leq 3$ -dimensional space setting. A fixed point procedure guarantees the existence...