On a Caginalp phase-field system with a logarithmic nonlinearity

Charbel Wehbe

Applications of Mathematics (2015)

  • Volume: 60, Issue: 4, page 355-382
  • ISSN: 0862-7940

Abstract

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We consider a phase field system based on the Maxwell Cattaneo heat conduction law, with a logarithmic nonlinearity, associated with Dirichlet boundary conditions. In particular, we prove, in one and two space dimensions, the existence of a solution which is strictly separated from the singularities of the nonlinear term and that the problem possesses a finite-dimensional global attractor in terms of exponential attractors.

How to cite

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Wehbe, Charbel. "On a Caginalp phase-field system with a logarithmic nonlinearity." Applications of Mathematics 60.4 (2015): 355-382. <http://eudml.org/doc/271609>.

@article{Wehbe2015,
abstract = {We consider a phase field system based on the Maxwell Cattaneo heat conduction law, with a logarithmic nonlinearity, associated with Dirichlet boundary conditions. In particular, we prove, in one and two space dimensions, the existence of a solution which is strictly separated from the singularities of the nonlinear term and that the problem possesses a finite-dimensional global attractor in terms of exponential attractors.},
author = {Wehbe, Charbel},
journal = {Applications of Mathematics},
keywords = {Caginalp phase-field system; Dirichlet boundary conditions; well-posedness; long time behavior of solution; global attractor; exponential attractor; Maxwell-Cattaneo law; logarithmic potential; Caginalp phase-field system; Dirichlet boundary conditions; well-posedness; long time behavior of solution; global attractor; exponential attractor; Maxwell-Cattaneo law; logarithmic potential},
language = {eng},
number = {4},
pages = {355-382},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On a Caginalp phase-field system with a logarithmic nonlinearity},
url = {http://eudml.org/doc/271609},
volume = {60},
year = {2015},
}

TY - JOUR
AU - Wehbe, Charbel
TI - On a Caginalp phase-field system with a logarithmic nonlinearity
JO - Applications of Mathematics
PY - 2015
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 60
IS - 4
SP - 355
EP - 382
AB - We consider a phase field system based on the Maxwell Cattaneo heat conduction law, with a logarithmic nonlinearity, associated with Dirichlet boundary conditions. In particular, we prove, in one and two space dimensions, the existence of a solution which is strictly separated from the singularities of the nonlinear term and that the problem possesses a finite-dimensional global attractor in terms of exponential attractors.
LA - eng
KW - Caginalp phase-field system; Dirichlet boundary conditions; well-posedness; long time behavior of solution; global attractor; exponential attractor; Maxwell-Cattaneo law; logarithmic potential; Caginalp phase-field system; Dirichlet boundary conditions; well-posedness; long time behavior of solution; global attractor; exponential attractor; Maxwell-Cattaneo law; logarithmic potential
UR - http://eudml.org/doc/271609
ER -

References

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