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Variational Problems with Concentration: 36 (Progress in Nonlinear Differential Equations and Their Applications, 36) - Hardcover
Synopsis
This self-contained research monograph focuses on semilinear Dirichlet problems and similar equations involving the p-Laplacian. The author explains new techniques in detail, and derives several numerical methods approximating the concentration point and the free boundary. The corresponding plots are highlights of this book.
"synopsis" may belong to another edition of this title.
Review
"This material is very rich, because various alternatives are possible. The book provides a good systematic overview of this difficult topic."
--Zentralblatt Math
Synopsis
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 text offers a detailed analysis of low-energy solutions. In PDE terms the low-energy limit corresponds to the well-known vanishing viscosity limit.
"About this title" may belong to another edition of this title.
- PublisherBirkhäuser
- Publication date1999
- ISBN 10 3764361360
- ISBN 13 9783764361365
- BindingHardcover
- LanguageEnglish
- Number of pages171
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Variational Problems with Concentration (Progress in Nonlinear Differential Equations and Their Applications)
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VARIATIONAL PROBLEMS WITH CONCENTRATION
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Variational Problems with Concentration (Progress in Nonlinear Differential Equations and Their Applications, 36)
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Variational Problems with Concentration
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Variational Problems with Concentration (Progress in Nonlinear Differential Equations and Their Applications, 36)
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Variational Problems with Concentration (Progress in Nonlinear Differential Equations and Their Applications, 36)
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Variational Problems with Concentration
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Springer, Basel, Birkhäuser Basel, Birkhäuser Jul 1999, 1999
ISBN 10: 3764361360
ISBN 13: 9783764361365
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Buch. Condition: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -To start with we describe two applications of the theory to be developed in this monograph: Bernoulli's free-boundary problem and the plasma problem. Bernoulli's free-boundary problem This problem arises in electrostatics, fluid dynamics, optimal insulation, and electro chemistry. In electrostatic terms the task is to design an annular con denser consisting of a prescribed conducting surface 80. and an unknown conduc tor A such that the electric field 'Vu is constant in magnitude on the surface 8A of the second conductor (Figure 1.1). This leads to the following free-boundary problem for the electric potential u. -~u 0 in 0. A, u 0 on 80., u 1 on 8A, 8u Q on 8A. 811 The unknowns are the free boundary 8A and the potential u. In optimal in sulation problems the domain 0. A represents the insulation layer. Given the exterior boundary 80. the problem is to design an insulating layer 0. A of given volume which minimizes the heat or current leakage from A to the environment ]R.n n. The heat leakage per unit time is the capacity of the set A with respect to n. Thus we seek to minimize the capacity among all sets A c 0. of equal volume. 163 pp. Englisch. Seller Inventory # 9783764361365
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Variational Problems with Concentration
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Buch. Condition: Neu. Druck auf Anfrage Neuware - Printed after ordering - To start with we describe two applications of the theory to be developed in this monograph: Bernoulli's free-boundary problem and the plasma problem. Bernoulli's free-boundary problem This problem arises in electrostatics, fluid dynamics, optimal insulation, and electro chemistry. In electrostatic terms the task is to design an annular con denser consisting of a prescribed conducting surface 80. and an unknown conduc tor A such that the electric field 'Vu is constant in magnitude on the surface 8A of the second conductor (Figure 1.1). This leads to the following free-boundary problem for the electric potential u. -~u 0 in 0. A, u 0 on 80., u 1 on 8A, 8u Q on 8A. 811 The unknowns are the free boundary 8A and the potential u. In optimal in sulation problems the domain 0. A represents the insulation layer. Given the exterior boundary 80. the problem is to design an insulating layer 0. A of given volume which minimizes the heat or current leakage from A to the environment ]R.n n. The heat leakage per unit time is the capacity of the set A with respect to n. Thus we seek to minimize the capacity among all sets A c 0. of equal volume. Seller Inventory # 9783764361365
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Variational Problems with Concentration
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Gebunden. Condition: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. This self-contained research monograph focuses on semilinear Dirichlet problems and similar equations involving the p-Laplacian. The author explains new techniques in detail, and derives several numerical methods approximating the concentration point and. Seller Inventory # 5279288
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Variational Problems with Concentration
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