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E-raamat: Asymptotic Issues For Some Partial Differential Equations

(Univ Zurich, Switzerland)
  • Formaat: 264 pages
  • Ilmumisaeg: 14-Jun-2016
  • Kirjastus: Imperial College Press
  • Keel: eng
  • ISBN-13: 9781783268931
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  • Formaat: 264 pages
  • Ilmumisaeg: 14-Jun-2016
  • Kirjastus: Imperial College Press
  • Keel: eng
  • ISBN-13: 9781783268931
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In an update of her 2002 Lambda Goes to Plus Infinity Chipot incorporates recent findings--her own and others'--in asymptotic issues for some partial differential equations. She covers the Dirichlet problem in some unbounded domains, the pure Neumann problem, periodic problems, anisotropic singular perturbation problems, eigenvalue problems, elliptic systems, the Stokes problem, variational inequalities, and the calculus of variations. The material could interest students and researchers in mathematics. Distributed in the US by World Scientific. Annotation ©2016 Ringgold, Inc., Portland, OR (protoview.com)

Much progress has been made in recent years on the issue of asymptotic behavior of problems set in bounded domains, for example cylinders. This book goes one step further by presenting the latest accomplishments on asymptotic behavior in domains which become unbounded.It also investigates new issues which have emerged including existence, anisotropic singular perturbation, periodic behavior forced by periodic data, and uniqueness theorem for problems set in unbounded domains. These new discoveries are treated with unique techniques developed to investigate the asymptotic behavior of variable problems.Theories investigated throughout the book can be applied to other problems related to partial differential equations, making it an important text for students and researchers within the discipline.Asymptotic Issues for Some Partial Differential Equations is an updated account of l Goes to Plus Infinity, published by Springer in 2002.
Foreword v
1 Introduction
1(46)
1.1 The Dirichlet problem
1(5)
1.2 Periodic problems
6(3)
1.3 Problems in unbounded domains
9(2)
1.4 Rescaling
11(1)
1.5 Eigenvalue problems
12(3)
1.6 Calculus of variations problems
15(4)
1.7 Parabolic problems
19(5)
1.8 Strongly nonlinear problems
24(5)
1.9 Higher order operators
29(4)
1.10 Higher order estimates
33(2)
1.11 Global convergence
35(2)
1.12 Correctors for the Dirichlet problem
37(10)
2 The Dirichlet problem in some unbounded domains
47(24)
2.1 The linear case
47(8)
2.2 A quasilinear case
55(9)
2.3 Pointwise convergence
64(7)
3 The pure Neumann problem
71(30)
3.1 Introduction
71(5)
3.2 Construction of a solution to the pure Neumann problem
76(11)
3.3 The case of data independent of x1
87(5)
3.4 The case with a lower order term
92(9)
4 Periodic problems
101(18)
4.1 A general theory
101(9)
4.2 Some degenerate case
110(3)
4.3 Application to the periodic obstacle problem
113(6)
5 Anisotropic singular perturbation problems
119(14)
5.1 Introduction
119(3)
5.2 Anisotropic singular perturbation problems
122(8)
5.3 Estimates for the rate of convergence
130(3)
6 Eigenvalue problems
133(32)
6.1 Introduction
133(1)
6.2 Convergence of the eigenvalues
134(10)
6.3 Convergence of the eigenfunctions
144(6)
6.4 An application
150(5)
6.5 The case of Neumann boundary conditions
155(10)
7 Elliptic systems
165(12)
7.1 Abstract formulation
165(4)
7.2 Some applications
169(8)
8 The Stokes problem
177(14)
8.1 Introduction and notation
177(2)
8.2 Auxiliary lemmas
179(2)
8.3 Main results
181(10)
9 Variational inequalities
191(22)
9.1 A simple result
191(3)
9.2 The obstacle problem in unbounded domains
194(11)
9.3 A general framework
205(6)
9.4 Some applications
211(2)
10 Calculus of variations
213(26)
10.1 Monotonicity properties
213(4)
10.2 A convergence result
217(13)
10.3 The case of the q-Laplace operator
230(9)
Some concluding remarks
237(2)
Appendix A
239(6)
A.1 Dictionary of the main notation
239(1)
A.2 Some existence results
240(3)
A.3 Poincare's Inequality
243(2)
Bibliography 245(6)
Index 251