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Author: I. V. Skrypnik Publisher: American Mathematical Soc. ISBN: 9780821897560 Category : Mathematics Languages : en Pages : 370
Book Description
The theory of nonlinear elliptic equations is currently one of the most actively developing branches of the theory of partial differential equations. This book investigates boundary value problems for nonlinear elliptic equations of arbitrary order. In addition to monotone operator methods, a broad range of applications of topological methods to nonlinear differential equations is presented: solvability, estimation of the number of solutions, and the branching of solutions of nonlinear equations. Skrypnik establishes, by various procedures, a priori estimates and the regularity of solutions of nonlinear elliptic equations of arbitrary order. Also covered are methods of homogenization of nonlinear elliptic problems in perforated domains. The book is suitable for use in graduate courses in differential equations and nonlinear functional analysis.
Author: I. V. Skrypnik Publisher: American Mathematical Soc. ISBN: 9780821897560 Category : Mathematics Languages : en Pages : 370
Book Description
The theory of nonlinear elliptic equations is currently one of the most actively developing branches of the theory of partial differential equations. This book investigates boundary value problems for nonlinear elliptic equations of arbitrary order. In addition to monotone operator methods, a broad range of applications of topological methods to nonlinear differential equations is presented: solvability, estimation of the number of solutions, and the branching of solutions of nonlinear equations. Skrypnik establishes, by various procedures, a priori estimates and the regularity of solutions of nonlinear elliptic equations of arbitrary order. Also covered are methods of homogenization of nonlinear elliptic problems in perforated domains. The book is suitable for use in graduate courses in differential equations and nonlinear functional analysis.
Author: Roland Glowinski Publisher: SIAM ISBN: 1611973783 Category : Mathematics Languages : en Pages : 473
Book Description
Variational Methods for the Numerical Solution of Nonlinear Elliptic Problems?addresses computational methods that have proven efficient for the solution of a large variety of nonlinear elliptic problems. These methods can be applied to many problems in science and engineering, but this book focuses on their application to problems in continuum mechanics and physics. This book differs from others on the topic by presenting examples of the power and versatility of operator-splitting methods; providing a detailed introduction to alternating direction methods of multipliers and their applicability to the solution of nonlinear (possibly nonsmooth) problems from science and engineering; and showing that nonlinear least-squares methods, combined with operator-splitting and conjugate gradient algorithms, provide efficient tools for the solution of highly nonlinear problems. The book provides useful insights suitable for advanced graduate students, faculty, and researchers in applied and computational mathematics as well as research engineers, mathematical physicists, and systems engineers.
Author: Ravi P Agarwal Publisher: World Scientific ISBN: 9814501859 Category : Mathematics Languages : en Pages : 606
Book Description
World Scientific Series in Applicable Analysis (WSSIAA) reports new developments of a high mathematical standard and of current interest. Each volume in the series is devoted to mathematical analysis that has been applied, or is potentially applicable to the solution of scientific, engineering, and social problems. The third volume of WSSIAA contains 47 research articles on inequalities by leading mathematicians from all over the world and a tribute by R.M. Redheffer to Wolfgang Walter — to whom this volume is dedicated — on his 66th birthday.Contributors: A Acker, J D Aczél, A Alvino, K A Ames, Y Avishai, C Bandle, B M Brown, R C Brown, D Brydak, P S Bullen, K Deimling, J Diaz, Á Elbert, P W Eloe, L H Erbe, H Esser, M Essén, W D Evans, W N Everitt, V Ferone, A M Fink, R Ger, R Girgensohn, P Goetgheluck, W Haussmann, S Heikkilä, J Henderson, G Herzog, D B Hinton, T Horiuchi, S Hu, B Kawohl, V G Kirby; N Kirchhoff, G H Knightly, H W Knobloch, Q Kong, H König, A Kufner, M K Kwong, A Laforgia, V Lakshmikantham, S Leela, R Lemmert, E R Love, G Lüttgens, S Malek, R Manásevich, J Mawhin, R Medina, M Migda, R J Nessel, Z Páles, N S Papageorgiou, L E Payne, J Pe…ariƒ, L E Persson, A Peterson, M Pinto, M Plum, J Popenda, G Porru, R M Redheffer, A A Sagle, S Saitoh, D Sather, K Schmitt, D F Shea, A Simon, S Sivasundaram, R Sperb, C S Stanton, G Talenti, G Trombetti, S Varošanec, A S Vatsala, P Volkmann, H Wang, V Weckesser, F Zanolin, K Zeller, A Zettl.
Author: Antonio Ambrosetti Publisher: Springer Science & Business Media ISBN: 0817681140 Category : Mathematics Languages : en Pages : 203
Book Description
This self-contained textbook provides the basic, abstract tools used in nonlinear analysis and their applications to semilinear elliptic boundary value problems and displays how various approaches can easily be applied to a range of model cases. Complete with a preliminary chapter, an appendix that includes further results on weak derivatives, and chapter-by-chapter exercises, this book is a practical text for an introductory course or seminar on nonlinear functional analysis.
Author: Hervé Le Dret Publisher: Springer ISBN: 3319783904 Category : Mathematics Languages : en Pages : 259
Book Description
This textbook presents the essential parts of the modern theory of nonlinear partial differential equations, including the calculus of variations. After a short review of results in real and functional analysis, the author introduces the main mathematical techniques for solving both semilinear and quasilinear elliptic PDEs, and the associated boundary value problems. Key topics include infinite dimensional fixed point methods, the Galerkin method, the maximum principle, elliptic regularity, and the calculus of variations. Aimed at graduate students and researchers, this textbook contains numerous examples and exercises and provides several comments and suggestions for further study.
Author: Ilya J. Bakelman Publisher: Springer Science & Business Media ISBN: 3642698816 Category : Mathematics Languages : en Pages : 524
Book Description
Investigations in modem nonlinear analysis rely on ideas, methods and prob lems from various fields of mathematics, mechanics, physics and other applied sciences. In the second half of the twentieth century many prominent, ex emplary problems in nonlinear analysis were subject to intensive study and examination. The united ideas and methods of differential geometry, topology, differential equations and functional analysis as well as other areas of research in mathematics were successfully applied towards the complete solution of com plex problems in nonlinear analysis. It is not possible to encompass in the scope of one book all concepts, ideas, methods and results related to nonlinear analysis. Therefore, we shall restrict ourselves in this monograph to nonlinear elliptic boundary value problems as well as global geometric problems. In order that we may examine these prob lems, we are provided with a fundamental vehicle: The theory of convex bodies and hypersurfaces. In this book we systematically present a series of centrally significant results obtained in the second half of the twentieth century up to the present time. Particular attention is given to profound interconnections between various divisions in nonlinear analysis. The theory of convex functions and bodies plays a crucial role because the ellipticity of differential equations is closely connected with the local and global convexity properties of their solutions. Therefore it is necessary to have a sufficiently large amount of material devoted to the theory of convex bodies and functions and their connections with partial differential equations.
Author: Athanasios S. Fokas Publisher: SIAM ISBN: 1611973813 Category : Mathematics Languages : en Pages : 290
Book Description
This book describes state-of-the-art advances and applications of the unified transform and its relation to the boundary element method. The authors present the solution of boundary value problems from several different perspectives, in particular the type of problems modeled by partial differential equations (PDEs). They discuss recent applications of the unified transform to the analysis and numerical modeling of boundary value problems for linear and integrable nonlinear PDEs and the closely related boundary element method, a well-established numerical approach for solving linear elliptic PDEs.? The text is divided into three parts. Part I contains new theoretical results on linear and nonlinear evolutionary and elliptic problems. New explicit solution representations for several classes of boundary value problems are constructed and rigorously analyzed. Part II is a detailed overview of variational formulations for elliptic problems. It places the unified transform approach in a classic context alongside the boundary element method and stresses its novelty. Part III presents recent numerical applications based on the boundary element method and on the unified transform.
Author: Dumitru Motreanu Publisher: Springer Science & Business Media ISBN: 1461493234 Category : Mathematics Languages : en Pages : 465
Book Description
This book focuses on nonlinear boundary value problems and the aspects of nonlinear analysis which are necessary to their study. The authors first give a comprehensive introduction to the many different classical methods from nonlinear analysis, variational principles, and Morse theory. They then provide a rigorous and detailed treatment of the relevant areas of nonlinear analysis with new applications to nonlinear boundary value problems for both ordinary and partial differential equations. Recent results on the existence and multiplicity of critical points for both smooth and nonsmooth functional, developments on the degree theory of monotone type operators, nonlinear maximum and comparison principles for p-Laplacian type operators, and new developments on nonlinear Neumann problems involving non-homogeneous differential operators appear for the first time in book form. The presentation is systematic, and an extensive bibliography and a remarks section at the end of each chapter highlight the text. This work will serve as an invaluable reference for researchers working in nonlinear analysis and partial differential equations as well as a useful tool for all those interested in the topics presented.
Author: I. V. Skrypnik
Author: I. V. Skrypnik
Author: Roland Glowinski
Author: Ravi P Agarwal
Author: Antonio Ambrosetti
Author: Hervé Le Dret
Author: H Begehr
Author: Ilya J. Bakelman
Author: Athanasios S. Fokas
Author: Pierre Grisvard
Author: Dumitru Motreanu