Singular Nonlinear Partial Differential Equations
Author | : Raymond Gerard |
Publisher | : |
Total Pages | : 284 |
Release | : 2014-01-15 |
Genre | : |
ISBN | : 9783322802859 |
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Author | : Raymond Gerard |
Publisher | : |
Total Pages | : 284 |
Release | : 2014-01-15 |
Genre | : |
ISBN | : 9783322802859 |
Author | : Raymond Gérard |
Publisher | : Springer Science & Business Media |
Total Pages | : 281 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 3322802841 |
The aim of this book is to put together all the results that are known about the existence of formal, holomorphic and singular solutions of singular non linear partial differential equations.
Author | : Gadi Fibich |
Publisher | : Springer |
Total Pages | : 870 |
Release | : 2015-03-06 |
Genre | : Mathematics |
ISBN | : 3319127489 |
This book is an interdisciplinary introduction to optical collapse of laser beams, which is modelled by singular (blow-up) solutions of the nonlinear Schrödinger equation. With great care and detail, it develops the subject including the mathematical and physical background and the history of the subject. It combines rigorous analysis, asymptotic analysis, informal arguments, numerical simulations, physical modelling, and physical experiments. It repeatedly emphasizes the relations between these approaches, and the intuition behind the results. The Nonlinear Schrödinger Equation will be useful to graduate students and researchers in applied mathematics who are interested in singular solutions of partial differential equations, nonlinear optics and nonlinear waves, and to graduate students and researchers in physics and engineering who are interested in nonlinear optics and Bose-Einstein condensates. It can be used for courses on partial differential equations, nonlinear waves, and nonlinear optics. Gadi Fibich is a Professor of Applied Mathematics at Tel Aviv University. “This book provides a clear presentation of the nonlinear Schrodinger equation and its applications from various perspectives (rigorous analysis, informal analysis, and physics). It will be extremely useful for students and researchers who enter this field.” Frank Merle, Université de Cergy-Pontoise and Institut des Hautes Études Scientifiques, France
Author | : Alexander A. Kovalevsky |
Publisher | : Walter de Gruyter GmbH & Co KG |
Total Pages | : 448 |
Release | : 2016-03-21 |
Genre | : Mathematics |
ISBN | : 3110332248 |
This monograph looks at several trends in the investigation of singular solutions of nonlinear elliptic and parabolic equations. It discusses results on the existence and properties of weak and entropy solutions for elliptic second-order equations and some classes of fourth-order equations with L1-data and questions on the removability of singularities of solutions to elliptic and parabolic second-order equations in divergence form. It looks at localized and nonlocalized singularly peaking boundary regimes for different classes of quasilinear parabolic second- and high-order equations in divergence form. The book will be useful for researchers and post-graduate students that specialize in the field of the theory of partial differential equations and nonlinear analysis. Contents: Foreword Part I: Nonlinear elliptic equations with L^1-data Nonlinear elliptic equations of the second order with L^1-data Nonlinear equations of the fourth order with strengthened coercivity and L^1-data Part II: Removability of singularities of the solutions of quasilinear elliptic and parabolic equations of the second order Removability of singularities of the solutions of quasilinear elliptic equations Removability of singularities of the solutions of quasilinear parabolic equations Quasilinear elliptic equations with coefficients from the Kato class Part III: Boundary regimes with peaking for quasilinear parabolic equations Energy methods for the investigation of localized regimes with peaking for parabolic second-order equations Method of functional inequalities in peaking regimes for parabolic equations of higher orders Nonlocalized regimes with singular peaking Appendix: Formulations and proofs of the auxiliary results Bibliography
Author | : Abduhamid Dzhuraev |
Publisher | : CRC Press |
Total Pages | : 220 |
Release | : 1999-11-29 |
Genre | : Science |
ISBN | : 9781584881445 |
Singular Partial Differential Equations provides an analytical, constructive, and elementary approach to non-elementary problems. In the first monograph to consider such equations, the author investigates the solvability of partial differential equations and systems in a class of bounded functions with complex coefficients having singularities at the inner points or boundary of the domain. Using complex variable techniques, the author considers a variety of problems, including the Dirichlet, Neumann, and other problems for first order systems. He also explores applications to singular equations, degenerate, high-dimensional Beltrami systems in Cn,, and others. Singular Partial Differential Equations fills a gap in the literature on degenerate and singular partial differential equations and significantly contributes to the theory of boundary value problems for these equations and systems. It will undoubtedly stimulate further research in the field. Practical applications in analysis and physics make this important reading for researchers and students in physics and engineering, along with mathematicians.
Author | : Mieczyslaw Altman |
Publisher | : World Scientific |
Total Pages | : 296 |
Release | : 1990 |
Genre | : Science |
ISBN | : 9789810203269 |
This research monograph offers a general theory which encompasses almost all known general theories in such a way that many practical applications can be obtained. It will be useful for mathematicians interested in the development of the abstract Control Theory with applications to Nonlinear PDE, as well as physicists, engineers, and economists looking for theoretical guidance in solving their optimal control problems; and graduate-level seminar courses in nonlinear applied functional analysis.
Author | : W. F. Ames |
Publisher | : Academic Press |
Total Pages | : 528 |
Release | : 1965-01-01 |
Genre | : Mathematics |
ISBN | : 008095524X |
Nonlinear Partial Differential Equations in Engineering
Author | : Huang Dun |
Publisher | : |
Total Pages | : 3 |
Release | : 1993 |
Genre | : |
ISBN | : |
Author | : Robert Hardt |
Publisher | : American Mathematical Soc. |
Total Pages | : 356 |
Release | : 1996 |
Genre | : Mathematics |
ISBN | : 9780821804315 |
This book contains lecture notes of minicourses at the Regional Geometry Institute at Park City, Utah, in July 1992. Presented here are surveys of breaking developments in a number of areas of nonlinear partial differential equations in differential geometry. The authors of the articles are not only excellent expositors, but are also leaders in this field of research. All of the articles provide in-depth treatment of the topics and require few prerequisites and less background than current research articles.
Author | : Shuxing Chen |
Publisher | : World Scientific |
Total Pages | : 207 |
Release | : 2010-09-24 |
Genre | : Mathematics |
ISBN | : 9814464996 |
The book provides a comprehensive overview on the theory on analysis of singularities for partial differential equations (PDEs). It contains a summarization of the formation, development and main results on this topic. Some of the author's discoveries and original contributions are also included, such as the propagation of singularities of solutions to nonlinear equations, singularity index and formation of shocks.