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Titlebook: Vortices in the Magnetic Ginzburg-Landau Model; Etienne Sandier,Sylvia Serfaty Textbook 2007 Birkh?user Boston 2007 functions of complex v

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書目名稱Vortices in the Magnetic Ginzburg-Landau Model
編輯Etienne Sandier,Sylvia Serfaty
視頻videohttp://file.papertrans.cn/986/985038/985038.mp4
概述Describes essential mathematical techniques and tools for analyzing the Ginzburg--Landau functional.Presents an introduction to the theory with results and current research.Acts a guide to the various
叢書名稱Progress in Nonlinear Differential Equations and Their Applications
圖書封面Titlebook: Vortices in the Magnetic Ginzburg-Landau Model;  Etienne Sandier,Sylvia Serfaty Textbook 2007 Birkh?user Boston 2007 functions of complex v
描述More than ten years have passed since the book of F. Bethuel, H. Brezis and F. H′ elein, which contributed largely to turning Ginzburg–Landau equations from a renowned physics model into a large PDE research ?eld, with an ever-increasing number of papers and research directions (the number of published mathematics papers on the subject is certainly in the several hundreds, and that of physics papers in the thousands). Having ourselves written a series of rather long and intricately - terdependent papers, and having taught several graduate courses and mini-courses on the subject, we felt the need for a more uni?ed and self-contained presentation. The opportunity came at the timely moment when Ha¨ ?m Brezis s- gested we should write this book. We would like to express our gratitude towards him for this suggestion and for encouraging us all along the way. As our writing progressed, we felt the need to simplify some proofs, improvesomeresults,aswellaspursuequestionsthatarosenaturallybut that we had not previously addressed. We hope that we have achieved a little bit of the original goal: to give a uni?ed presentation of our work with a mixture of both old and new results, and provide a
出版日期Textbook 2007
關(guān)鍵詞functions of complex variables; mathematical physics; model; partial differential equation; partial diff
版次1
doihttps://doi.org/10.1007/978-0-8176-4550-2
isbn_ebook978-0-8176-4550-2Series ISSN 1421-1750 Series E-ISSN 2374-0280
issn_series 1421-1750
copyrightBirkh?user Boston 2007
The information of publication is updating

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Branches of Solutions,t of the matter consists in proving that the minimum is achieved in the interior of ., thus yielding locally minimizing solutions of the equations. These solutions turn out to be global energy minimizers in some narrow intervals of values of ..
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,Physical Presentation of the Model—Critical Fields,the physics literature. We will also give a nonrigorous introduction to critical fields in ?., in the spirit of Abrikosov, and draw a corresponding phase diagram in the (.) plane, i.e., qualitatively describe minimizers of the Ginzburg-Landau energy for different values of . and ., emphasizing the r
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Higher Values of the Applied Field,tically like λ|log .|, letting λ → ∞ in Theorem 7.2 indicates that for energy-minimizers for applied fields . ? |log .|, we must have .. But in this regime, . and the arguments of Chapter 7 do not give, even formally, the leading order term of the minimal energy. Moreover, the tools which were at th
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