Existence of Minimizer to the Ginzburg-Landau Free Energy of Ferromagnetic System

Article Preview

Abstract:

In this paper, we obtain the existence of minimizer to Ginzburg-Landau free energy of ferromagnetic system by coercivity and weakly lower semi-continuity of the free energy, where the weakly lower semi-continuity is derived from monotone operator condition and the Sobolev space compact imbedding theorem.

You might also be interested in these eBooks

Info:

Periodical:

Pages:

717-722

Citation:

Online since:

October 2013

Authors:

Export:

Price:

Permissions CCC:

Permissions PLS:

Сopyright:

© 2014 Trans Tech Publications Ltd. All Rights Reserved

Share:

Citation:

[1] C. B. Morrey, Quasiconvexity and the semicontinuity of multiple integrals. Pacific Journal of Mathematics, Vol. 2, no. 2, pp.25-53, (1952).

Google Scholar

[2] E. Acerbi and N. Fusco, Semicontinuity problems in the calculus of variations, Archive for Rational Mechanics and Analysis. Vol. 86, no. 2, pp.125-145, (1984).

DOI: 10.1007/bf00275731

Google Scholar

[3] O. Kovacik and J. Rakosnik, On spacesand, Czechoslovak Mathematical Journal, Vol. 41, Issue 4, pp.592-618, (1991).

Google Scholar

[4] L. Diening, P. Harjulehto, P. Hasto. and M. Ruzicka, Lebesgue and Sobolev Spaces with Variable Exponents, Springer, Berlin, Germany, (2011).

DOI: 10.1007/978-3-642-18363-8

Google Scholar

[5] D. Edmunds and Rakosnik, Sobolev embedding with variable exponent, Studia Mathematica, Vol. 143, no. 3, pp.267-293, (2000).

DOI: 10.4064/sm-143-3-267-293

Google Scholar

[6] D. Edmunds and Rakosnik, Sobolev embedding with variable exponent II, Mathematische Nachrichten, " Vol. 246-247, Issue 1, pp.53-67, (2002).

Google Scholar

[7] Y. Q. Fu, Weak lower semicontinuity of variational functionals with variable growth, Journal of Inequalities and Applications, Vol. 2011, no. 1, pp.1-19, (2011).

DOI: 10.1186/1029-242x-2011-19

Google Scholar

[8] Y. M. Long and S. Q Zhang, Geometric characterizations for variational minimization solutions of the 3-Body Problem,Acta Mathematica Sinica, English Series, Vol. 16, no. 4, pp.579-592, (2000).

DOI: 10.1007/s101140000007

Google Scholar

[9] S. Q Zhang, Q. Zhou, Variational methods for the choreography solution to the three-body problem, Science in China, Vol. 45 No. 5, pp.594-597, (2002).

Google Scholar

[10] A. Onuki, Phase transition dynamics, Cambridge University Press, (2007).

Google Scholar

[11] T. Ma, Partial differential equation theory and method, Science Press, (2011).

Google Scholar

[12] T. Ma and S. H. Wang, Dynamic phase transitions for ferromagnetic systems, Journal of Mathematical Physics, Vol. 49, no. 5, pp.053506-18, (2008).

Google Scholar

[13] T. Ma and S. H. Wang, Phase Transition Dynamics in Nonlinear Sciences, Springer, New York, (2012).

Google Scholar

[14] L. C. Evens, Partial Differential Equations, American Mathematical Society, Providence, Rhode Island, (1998).

Google Scholar

[15] R. A. Adams, Sobolev Space, Pure and Applied Mathematics, Vol. 6, Academic Press, London, UK, (1975).

Google Scholar