Item description for Variational Problems with Concentration (Progress in Nonlinear Differential Equations and Their Applications) by Martin Flucher...
The subject of this research monograph is semilinear Dirichlet problems and similar equations involving the p-Laplacian. Solutions are constructed by a constraint variational method. The major new contribution is a detailed analysis of low-energy solutions. In PDE terms the low-energy limit corresponds to the well-known vanishing viscosity limit.
First it is shown that in the low-energy limit the Dirichlet energy concentrates at a single point in the domain. This behaviour is typical of a large class of nonlinearities known as zero mass case. Moreover, the concentration point can be identified in geometrical terms. This fact is essential for flux minimization problems. Finally, the asymptotic behaviour of low-energy solutions in the vicinity of the concentration point is analyzed on a microscopic scale.
The sound analysis of the zero mass case is novel and complementary to the majority of research articles dealing with the positive mass case. It illustrates the power of a purely variational approach where PDE methods run into technical difficulties. To the readers' benefit, the presentation is self-contained and new techniques are explained in detail.
Bernoulli's free-boundary problem and the plasma problem are the principal applications to which the theory is applied. The author derives several numerical methods approximating the concentration point and the free boundary. These methods have been implemented and tested by a co-worker. The corresponding plots are highlights of this book.
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Est. Packaging Dimensions: Length: 9.3" Width: 6.4" Height: 0.7" Weight: 0.95 lbs.
Release Date Sep 24, 1999
Publisher Birkhäuser Basel
ISBN 3764361360 ISBN13 9783764361365
Availability 81 units. Availability accurate as of Oct 24, 2016 06:20.
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