On a phase-field model with a logarithmic nonlinearity

Alain Miranville

Applications of Mathematics (2012)

  • Volume: 57, Issue: 3, page 215-229
  • ISSN: 0862-7940

Abstract

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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.

How to cite

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Miranville, Alain. "On a phase-field model with a logarithmic nonlinearity." Applications of Mathematics 57.3 (2012): 215-229. <http://eudml.org/doc/247184>.

@article{Miranville2012,
abstract = {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.},
author = {Miranville, Alain},
journal = {Applications of Mathematics},
keywords = {phase field system; Maxwell-Cattaneo law; well-posedness; logarithmic potential; phase field system; Maxwell-Cattaneo law; well-posedness; logarithmic potential},
language = {eng},
number = {3},
pages = {215-229},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On a phase-field model with a logarithmic nonlinearity},
url = {http://eudml.org/doc/247184},
volume = {57},
year = {2012},
}

TY - JOUR
AU - Miranville, Alain
TI - On a phase-field model with a logarithmic nonlinearity
JO - Applications of Mathematics
PY - 2012
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 57
IS - 3
SP - 215
EP - 229
AB - 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.
LA - eng
KW - phase field system; Maxwell-Cattaneo law; well-posedness; logarithmic potential; phase field system; Maxwell-Cattaneo law; well-posedness; logarithmic potential
UR - http://eudml.org/doc/247184
ER -

References

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