Global solution to a generalized nonisothermal Ginzburg-Landau system

Nesrine Fterich

Applications of Mathematics (2010)

  • Volume: 55, Issue: 1, page 1-46
  • ISSN: 0862-7940

Abstract

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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, 5 (2005), 753–768. The existence of solutions to a related Neumann-Robin problem is established in an N ≤ 3 -dimensional space setting. A fixed point procedure guarantees the existence of solutions locally in time. Next, Sobolev embeddings, interpolation inequalities, Moser iterations estimates and results on renormalized solutions for a parabolic equation with L 1 data are used to handle a suitable a priori estimate which allows to extend our local solutions to the whole time interval. The uniqueness result is justified by proper contracting estimates.

How to cite

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Fterich, Nesrine. "Global solution to a generalized nonisothermal Ginzburg-Landau system." Applications of Mathematics 55.1 (2010): 1-46. <http://eudml.org/doc/37837>.

@article{Fterich2010,
abstract = {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, 5 (2005), 753–768. The existence of solutions to a related Neumann-Robin problem is established in an $N \le 3$-dimensional space setting. A fixed point procedure guarantees the existence of solutions locally in time. Next, Sobolev embeddings, interpolation inequalities, Moser iterations estimates and results on renormalized solutions for a parabolic equation with $L^1$ data are used to handle a suitable a priori estimate which allows to extend our local solutions to the whole time interval. The uniqueness result is justified by proper contracting estimates.},
author = {Fterich, Nesrine},
journal = {Applications of Mathematics},
keywords = {nonisothermal Ginzburg-Landau (Allen-Cahn) system; microforce balance; existence and uniqueness results; renormalized solutions; Moser iterations; nonisothermal Ginzburg-Landau (Allen-Cahn) system; microforce balance; existence; uniqueness; renormalized solution; Moser iterations},
language = {eng},
number = {1},
pages = {1-46},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Global solution to a generalized nonisothermal Ginzburg-Landau system},
url = {http://eudml.org/doc/37837},
volume = {55},
year = {2010},
}

TY - JOUR
AU - Fterich, Nesrine
TI - Global solution to a generalized nonisothermal Ginzburg-Landau system
JO - Applications of Mathematics
PY - 2010
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 55
IS - 1
SP - 1
EP - 46
AB - 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, 5 (2005), 753–768. The existence of solutions to a related Neumann-Robin problem is established in an $N \le 3$-dimensional space setting. A fixed point procedure guarantees the existence of solutions locally in time. Next, Sobolev embeddings, interpolation inequalities, Moser iterations estimates and results on renormalized solutions for a parabolic equation with $L^1$ data are used to handle a suitable a priori estimate which allows to extend our local solutions to the whole time interval. The uniqueness result is justified by proper contracting estimates.
LA - eng
KW - nonisothermal Ginzburg-Landau (Allen-Cahn) system; microforce balance; existence and uniqueness results; renormalized solutions; Moser iterations; nonisothermal Ginzburg-Landau (Allen-Cahn) system; microforce balance; existence; uniqueness; renormalized solution; Moser iterations
UR - http://eudml.org/doc/37837
ER -

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