Displaying similar documents to “A semidiscretization scheme for a phase-field type model for solidification.”

On the Caginalp system with dynamic boundary conditions and singular potentials

Laurence Cherfils, Alain Miranville (2009)

Applications of Mathematics

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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...

Stability of hydrodynamic model for semiconductor

Massimiliano Daniele Rosini (2005)

Archivum Mathematicum

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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.

On a phase-field model with a logarithmic nonlinearity

Alain Miranville (2012)

Applications of Mathematics

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Our aim in this paper is to study the existence of solutions to a phase-field system based on the Maxwell-Cattaneo heat conduction law, with a logarithmic nonlinearity. In particular, we prove, in one and two space dimensions, the existence of a solution which is separated from the singularities of the nonlinear term.