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Langue: anglais
Edité par Springer, 2009
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Ajouter au panierEtat : New. Contains plenty of examples and exercisesIncludes new results which have not been previously presented in book formContains plenty of examples and exercisesIncludes new results which have not been previously presented in book for.
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Edité par Springer New York, Springer US Nov 2010, 2010
ISBN 10 : 1441927441 ISBN 13 : 9781441927446
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Ajouter au panierTaschenbuch. Etat : Neu. Neuware -How to solve partial differential systems by completing the square. This could well have been the title of this monograph as it grew into a project to develop a s- tematic approach for associating suitable nonnegative energy functionals to a large class of partial differential equations (PDEs) and evolutionary systems. The minima of these functionals are to be the solutions we seek, not because they are critical points (i. e. , from the corresponding Euler-Lagrange equations) but from also - ing zeros of these functionals. The approach can be traced back to Bogomolnyi¿s trick of ¿completing squares¿ in the basic equations of quantum eld theory (e. g. , Yang-Mills, Seiberg-Witten, Ginzburg-Landau, etc. ,), which allows for the deri- tion of the so-called self (or antiself) dual version of these equations. In reality, the ¿self-dual Lagrangians¿ we consider here were inspired by a variational - proach proposed ¿ over 30 years ago ¿ by Brezis ¿ and Ekeland for the heat equation and other gradient ows of convex energies. It is based on Fenchel-Legendre - ality and can be used on any convex functional ¿ not just quadratic ones ¿ making them applicable in a wide range of problems. In retrospect, we realized that the ¿- ergy identities¿ satis ed by Leray¿s solutions for the Navier-Stokes equations are also another manifestation of the concept of self-duality in the context of evolution equations.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 368 pp. Englisch.