Geodesic
Global solution to a generalized nonisothermal Ginzburg-Landau system
Applications of Mathematics, Tome 55 (2010) no. 1, pp. 1-46 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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, {\it 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.
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, {\it 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.
DOI : 10.1007/s10492-010-0001-0
Classification : 35K55, 35Q56, 80A22
Keywords: nonisothermal Ginzburg-Landau (Allen-Cahn) system; microforce balance; existence and uniqueness results; renormalized solutions; Moser iterations 
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     author = {Fterich, Nesrine},
     title = {Global solution to a generalized nonisothermal {Ginzburg-Landau} system},
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     pages = {1--46},
     year = {2010},
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     zbl = {1224.35388},
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Fterich, Nesrine. Global solution to a generalized nonisothermal Ginzburg-Landau system. Applications of Mathematics, Tome 55 (2010) no. 1, pp. 1-46. doi: 10.1007/s10492-010-0001-0

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