Stuart S. Antman - Böcker

This IMA Volume in Mathematics and its Applications Metastability and Incompletely Posed Problems represents the proceedings of a workshop which was an integral part of the 19R4-R5 IMA program on CONTINUUM PHYSICS AND PARTIAL DIFFERENTIAL EOIIATIONS. We are grateful to the Scientific Committee: ,I.L. Eri cksen D. Kinderlehrer H. Rrezis C. Dafermos for their dedication and hard work in developing an imaginative, stimulating, and productive year-long program. George R. Sell Hans Weinberger Preface Most equilibrium events in nature do not realize configurations of minimum energy. They are only metastable. Available knowledge of constitutive relations and environmental interactions may be limiterl. As a result, many configurations may he compatible with the rlata. Such questions are incompletely poserl. The papers in this volume address a wide variety of these issues as they are perceived by the material scientist and the mathematician. They represent a portion of the significant activity which has been underway in recent years, from the experimental arena and physical theory to the analysis of differential equations and computation.

This monograph, the first of the two volumes forming the third edition, is an enlarged, completely updated, and extensively revised version of the corresponding material from the authoritative second edition. This volume is devoted to the careful formulation and detailed study of illuminating geometrically and mechanically exact problems for nonlinearly elastic and viscoelastic strings, cables, rods, and shells. Special emphasis is placed on the role of nonlinear material response. Global bifurcation theory, direct methods of the calculus of variations, and dynamical methods, which are applied to these problems, are given self-contained presentations in the text and in the appendices.Each chapter contains a wealth of interesting, challenging, and tractable exercises.From the reviews of the second edition:"This second edition accounts for the developments since the first edition was published and differs from the first edition in many points. The book has been reorganized and several parts have been added. … The already impressive body of references has been further expanded. The reviewer highly recommends this book both to graduate students and to scholars interested in the theory of elasticity." (Massimo Lanza de Cristoforis, Mathematical Reviews, Issue 2006e:74001)"The second extended edition of the reviewed monograph gives a fundamental presentation of problems of nonlinear elasticity. Every chapter is equipped by instructive exercises, unsolved problems and exhaustive historical comments. The book could be very useful to applied mathematicians and engineers using in their works the elasticity theory and … to specialists dealing with applications of differential equations and bifurcation theory." (Boris V. Loginov, Zentralblatt MATH, Vol. 1098 (24), 2006)"Antman’s impressive work is … a comprehensive treatise on nonlinear elasticity and a quintessential example of applied nonlinearanalysis. … The text has been revised and updated, several new sections have been added … This book is a ‘must’ for researchers and graduate students interested in nonlinear continuum mechanics and applied analysis. The work is scholarly and well written. … ‘This book is directed toward scientists, engineers, and mathematicians who wish to see careful treatments of uncompromised problems.’" (Timothy J. Healey, SIAM Review, Vol. 49 (2), 2007)

This monograph, the second of the two volumes forming the third edition, is an enlarged, completely updated, and extensively revised version of the corresponding material from the authoritative second edition. It is completely self-contained. This volume contains chapters on tensors, three-dimensional continuum mechanics, constitutive equations and their physically natural restrictions for three-dimensional elasticity and strain-rate viscoelasticity, steady-state and dynamical problems for these theories, general geometrically and mechanically exact theories of rods and shells, methods for treating dynamical problems of strain-rate viscoelasticity, and the role of material response for quasilinear hyperbolic systems of elasticity. Each chapter contains a wealth of interesting, challenging, and tractable exercises.From the reviews of the second edition:"This second edition accounts for the developments since the first edition was published, and differs from the first edition in many points. The book has been reorganized and several parts have been added. … The already impressive body of references has been further expanded. The reviewer highly recommends this book both to graduate students and to scholars interested in the theory of elasticity." (Massimo Lanza de Cristoforis, Mathematical Reviews, Issue 2006e:74001)"The second extended edition of the reviewed monograph gives a fundamental presentation of problems of nonlinear elasticity. Every chapter is equipped by instructive exercises, unsolved problems and exhaustive historical comments. The book could be very useful to applied mathematicians and engineers using in their works the elasticity theory and … to specialists dealing with applications of differential equations and bifurcation theory." (Boris V. Loginov, Zentralblatt MATH, Vol. 1098 (24), 2006)"Antman’s impressive work is … a comprehensivetreatise on nonlinear elasticity and a quintessential example of applied nonlinear analysis. … The text has been revised and updated, Several new sections have been added … This book is a ‘must’ for researchers and graduate students interested in nonlinear continuum mechanics and applied analysis. The work is scholarly and well written. … ‘This book is directed toward scientists, engineers, and mathematicians who wish to see careful treatments of uncompromised problems.’" (Timothy J. Healey, SIAM Review, Vol. 49 (2), 2007)