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Global solution to a generalized nonisothermal Ginzburg-Landau system

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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 ⩽ 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.

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  1. Laboratoire de Mathématiques et Applications, UMR CNRS 6086, Université de Poitiers-SP2MI, Boulevard Marie et Pierre Curie, F-86962, Chasseneuil Futuroscope Cedex, France

    Nesrine Fterich

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  1. Nesrine Fterich
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Fterich, N. Global solution to a generalized nonisothermal Ginzburg-Landau system. Appl Math 55, 1–46 (2010). https://doi.org/10.1007/s10492-010-0001-0

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