Boundary-Interior Layer Interactions in Nonlinear Singular Perturbation Theory PDF Download
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Author: Frederick A. Howes Publisher: American Mathematical Soc. ISBN: 0821822039 Category : Boundary value problems Languages : en Pages : 116
Book Description
For three classes of singularly perturbed boundary value problems we study the existence of solutions which possess boundary, shock and corner layer behavior and we examine how these nonuniformities arise and how they influence one another. The keys to our analysis are the stability properties of solutions of corresponding reduced problems and the geometric properties of solutions of the boundary value problems inside such layers. Several examples of the theory are discussed in detail with a view to illustrating the naturalness of our approach.
Author: Frederick A. Howes Publisher: American Mathematical Soc. ISBN: 0821822039 Category : Boundary value problems Languages : en Pages : 116
Book Description
For three classes of singularly perturbed boundary value problems we study the existence of solutions which possess boundary, shock and corner layer behavior and we examine how these nonuniformities arise and how they influence one another. The keys to our analysis are the stability properties of solutions of corresponding reduced problems and the geometric properties of solutions of the boundary value problems inside such layers. Several examples of the theory are discussed in detail with a view to illustrating the naturalness of our approach.
Author: K. W. Chang Publisher: Springer Science & Business Media ISBN: 146121114X Category : Mathematics Languages : en Pages : 191
Book Description
Our purpose in writing this monograph is twofold. On the one hand, we want to collect in one place many of the recent results on the exist ence and asymptotic behavior of solutions of certain classes of singularly perturbed nonlinear boundary value problems. On the other, we hope to raise along the way a number of questions for further study, mostly ques tions we ourselves are unable to answer. The presentation involves a study of both scalar and vector boundary value problems for ordinary dif ferential equations, by means of the consistent use of differential in equality techniques. Our results for scalar boundary value problems obeying some type of maximum principle are fairly complete; however, we have been unable to treat, under any circumstances, problems involving "resonant" behavior. The linear theory for such problems is incredibly complicated already, and at the present time there appears to be little hope for any kind of general nonlinear theory. Our results for vector boundary value problems, even those admitting higher dimensional maximum principles in the form of invariant regions, are also far from complete. We offer them with some trepidation, in the hope that they may stimulate further work in this challenging and important area of differential equa tions. The research summarized here has been made possible by the support over the years of the National Science Foundation and the National Science and Engineering Research Council.
Author: Donald R. Smith Publisher: Cambridge University Press ISBN: 9780521300421 Category : Mathematics Languages : en Pages : 532
Book Description
Introduction to singular perturbation problems. Since the nature of the nonuniformity can vary from case to case, the author considers and solves a variety of problems, mostly for ordinary differential equations.
Author: Carmelo Clavero Publisher: Springer Science & Business Media ISBN: 3642196659 Category : Mathematics Languages : en Pages : 259
Book Description
This volume will contain selected papers from the lectures held at the BAIL 2010 Conference, which took place from July 5th to 9th, 2010 in Zaragoza (Spain). The papers present significant advances in the modeling, analysis and construction of efficient numerical methods to solve boundary and interior layers appearing in singular perturbation problems. Special emphasis is put on the mathematical foundations of such methods and their application to physical models. Topics in scientific fields such as fluid dynamics, quantum mechanics, semiconductor modeling, control theory, elasticity, chemical reactor theory, and porous media are examined in detail.
Author: Robert E. O'Malley Publisher: Springer ISBN: 3319119249 Category : Mathematics Languages : en Pages : 263
Book Description
This engaging text describes the development of singular perturbations, including its history, accumulating literature, and its current status. While the approach of the text is sophisticated, the literature is accessible to a broad audience. A particularly valuable bonus are the historical remarks. These remarks are found throughout the manuscript. They demonstrate the growth of mathematical thinking on this topic by engineers and mathematicians. The book focuses on detailing how the various methods are to be applied. These are illustrated by a number and variety of examples. Readers are expected to have a working knowledge of elementary ordinary differential equations, including some familiarity with power series techniques, and of some advanced calculus. Dr. O'Malley has written a number of books on singular perturbations. This book has developed from many of his works in the field of perturbation theory.
Author: Valarmathi Sigamani Publisher: Springer ISBN: 8132235983 Category : Mathematics Languages : en Pages : 172
Book Description
This book offers an ideal introduction to singular perturbation problems, and a valuable guide for researchers in the field of differential equations. It also includes chapters on new contributions to both fields: differential equations and singular perturbation problems. Written by experts who are active researchers in the related fields, the book serves as a comprehensive source of information on the underlying ideas in the construction of numerical methods to address different classes of problems with solutions of different behaviors, which will ultimately help researchers to design and assess numerical methods for solving new problems. All the chapters presented in the volume are complemented by illustrations in the form of tables and graphs.
Author: Frederick A. Howes
Author: Frederick A. Howes
Author: K. W. Chang
Author: Donald R. Smith
Author: Carmelo Clavero
Author: M.D. Ardema
Author: Ferdinand Verhulst
Author: 
Author: Robert E. O'Malley
Author: Valarmathi Sigamani
Author: Louis R. Hunt