Asymptotic Issues for Some Partial Differential Equations Second Edition by Michel Marie Chipot ISBN 978-9811290435 9811290431
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Product details:
ISBN 10: 9811290431
ISBN 13: 978-9811290435
Author: Michel Marie. Chipot
Review of the First Edition: “The monograph is well written and organized and recommended to graduate students and researchers in applied mathematics or engineering.” Zentralblatt MATH The primary focus of the book is to explore the asymptotic behavior of problems formulated within cylindrical structures. Various physical applications are discussed, with certain topics such as fluid flows in channels being particularly noteworthy. Additionally, the book delves into the relevance of elasticity in the context of cylindrical bodies. In specific scenarios where the size of the cylinder becomes exceptionally large, the material’s behavior is determined solely by its cross-section. The investigation centers around understanding these particular properties. Since the publication of the first edition, several significant advancements have been made, adding depth and interest to the content. Consequently, new sections have been incorporated into the existing edition, complemented by a comprehensive list of references.
Table of contents:
1. Introduction
1.1 The Dirichlet problem
1.2 Periodic problems.
1.3 Problems in unbounded domains
1.4 Rescaling
1.5 Eigenvalue problems
1.6 Pointwise convergence technique
1.7 Calculus of variations problems
1.8 Parabolic problems
1.9 Strongly nonlinear problems
1.10 Higher order operators
1.11 Higher order estimates
1.12 Global convergence
1.13 Correctors for the Dirichlet problem
2. The Dirichlet problem in some unbounded domains
2.1 The linear case
2.2 A quasilinear case
2.3 Pointwise convergence
2.4 Global convergence
3. The pure Neumann problem
3.1 Introduction
3.2 The case p = 1
3.3 The case of data independent of 21
3.4 A case p>1.
3.5 The case with a lower order term
4. Periodic problems
4.1 A general theory
4.2 Some degenerate case
4.3 Application to the periodic obstacle problem.
4.4 The Neumann periodic case
5. Anisotropic singular perturbation problems
5.1 Introduction
5.2 Anisotropic singular perturbation problems
5.3 Estimates for the rate of convergence
5.4 A pure Neumann case
6. Eigenvalue problems
6.1 Introduction
6.2 Convergence of the eigenvalues
6.3 Convergence of the eigenfunctions
6.4 An application
6.5 The case of Neumann boundary conditions.
7. Elliptic systems
7.1 Abstract formulation
7.2 Some applications.
8. The Stokes problem
8.1 Introduction and notation
8.2 Auxiliary lemmas
8.3 Main results
8.4 Remark on the Poiseuille flow
8.5 Global convergence
9. Variational inequalities
9.1 A simple result
9.2 The obstacle problem in unbounded domains
9.3 A general framework
9.4 Some applications.
10. Calculus of variations
10.1 Monotonicity properties
10.2 A convergence result
10.3 The case of the q-Laplace operator
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Tags: Michel Marie. Chipot, Asymptotic Issues, Some Partial Differential