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Author: Andrew Majda
Publisher: American Mathematical Soc.
Published: 1983
Total Pages: 102
ISBN-13: 0821822756
DOWNLOAD EBOOKA systematic study of the linearized stability of multi-dimensional shock-front solutions of a system of hyperbolic conservation laws is developed.
Author: Andrew Majda
Publisher: American Mathematical Soc.
Published: 1983
Total Pages: 102
ISBN-13: 0821822810
DOWNLOAD EBOOKThe short-time existence of discontinuous shock front solutions of a system of conservation laws in several space variables is proved below under suitable hypotheses. These shock front solutions are nonlinear progressing wave solutions associated with the nonlinear wave fields. The results developed here apply to the equations of compressible fluid flow in two or three space variables with standard equations of state where the initial data can have shock discontinuities of arbitrary strength which lie on a given smooth initial surface with arbitrary geometry.
Author: C.M. Dafermos
Publisher: Gulf Professional Publishing
Published: 2005-11-30
Total Pages: 684
ISBN-13: 9780444520487
DOWNLOAD EBOOKThis book contains several introductory texts concerning the main directions in the theory of evolutionary partial differential equations. The main objective is to present clear, rigorous, and in depth surveys on the most important aspects of the present theory.
Author: Shuichi Kawashima
Publisher: World Scientific
Published: 1998
Total Pages: 378
ISBN-13: 9789810233969
DOWNLOAD EBOOKIn the past two decades, there has been great progress in the theory of nonlinear partial differential equations. This book describes the progress, focusing on interesting topics in gas dynamics, fluid dynamics, elastodynamics etc. It contains ten articles, each of which discusses a very recent result obtained by the author. Some of these articles review related results.
Author: Michael Demuth
Publisher: Birkhäuser
Published: 2012-12-06
Total Pages: 346
ISBN-13: 3034882319
DOWNLOAD EBOOKThe intention of the international conference PDE2000 was to bring together specialists from different areas of modern analysis, mathematical physics and geometry, to discuss not only the recent progress in their own fields but also the interaction between these fields. The special topics of the conference were spectral and scattering theory, semiclassical and asymptotic analysis, pseudodifferential operators and their relation to geometry, as well as partial differential operators and their connection to stochastic analysis and to the theory of semigroups. The scientific advisory board of the conference in Clausthal consisted of M. Ben-Artzi (Jerusalem), Chen Hua (Peking), M. Demuth (Clausthal), T. Ichinose (Kanazawa), L. Rodino (Turin), B.-W. Schulze (Potsdam) and J. Sjöstrand (Paris). The book is aimed at researchers in mathematics and mathematical physics with interests in partial differential equations and all its related fields.
Author: Denis Serre
Publisher: Cambridge University Press
Published: 1999-05-27
Total Pages: 290
ISBN-13: 9781139425414
DOWNLOAD EBOOKSystems of conservation laws arise naturally in physics and chemistry. To understand them and their consequences (shock waves, finite velocity wave propagation) properly in mathematical terms requires, however, knowledge of a broad range of topics. This book sets up the foundations of the modern theory of conservation laws, describing the physical models and mathematical methods, leading to the Glimm scheme. Building on this the author then takes the reader to the current state of knowledge in the subject. The maximum principle is considered from the viewpoint of numerical schemes and also in terms of viscous approximation. Small waves are studied using geometrical optics methods. Finally, the initial-boundary problem is considered in depth. Throughout, the presentation is reasonably self-contained, with large numbers of exercises and full discussion of all the ideas. This will make it ideal as a text for graduate courses in the area of partial differential equations.
Author: Björn Engquist
Publisher: Springer
Published: 2017-04-05
Total Pages: 1219
ISBN-13: 364256478X
DOWNLOAD EBOOKThis is a book guaranteed to delight the reader. It not only depicts the state of mathematics at the end of the century, but is also full of remarkable insights into its future de- velopment as we enter a new millennium. True to its title, the book extends beyond the spectrum of mathematics to in- clude contributions from other related sciences. You will enjoy reading the many stimulating contributions and gain insights into the astounding progress of mathematics and the perspectives for its future. One of the editors, Björn Eng- quist, is a world-renowned researcher in computational sci- ence and engineering. The second editor, Wilfried Schmid, is a distinguished mathematician at Harvard University. Likewi- se the authors are all foremost mathematicians and scien- tists, and their biographies and photographs appear at the end of the book. Unique in both form and content, this is a "must-read" for every mathematician and scientist and, in particular, for graduates still choosing their specialty. Limited collector's edition - an exclusive and timeless work. This special, numbered edition will be available until June 1, 2000. Firm orders only.
Author: S. Friedlander
Publisher: Elsevier
Published: 2004-10-06
Total Pages: 687
ISBN-13: 0080472915
DOWNLOAD EBOOKThe Handbook of Mathematical Fluid Dynamics is a compendium of essays that provides a survey of the major topics in the subject. Each article traces developments, surveys the results of the past decade, discusses the current state of knowledge and presents major future directions and open problems. Extensive bibliographic material is provided. The book is intended to be useful both to experts in the field and to mathematicians and other scientists who wish to learn about or begin research in mathematical fluid dynamics. The Handbook illuminates an exciting subject that involves rigorous mathematical theory applied to an important physical problem, namely the motion of fluids.
Author: Heinrich Freistühler
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 527
ISBN-13: 1461201934
DOWNLOAD EBOOKIn the field known as "the mathematical theory of shock waves," very exciting and unexpected developments have occurred in the last few years. Joel Smoller and Blake Temple have established classes of shock wave solutions to the Einstein Euler equations of general relativity; indeed, the mathematical and physical con sequences of these examples constitute a whole new area of research. The stability theory of "viscous" shock waves has received a new, geometric perspective due to the work of Kevin Zumbrun and collaborators, which offers a spectral approach to systems. Due to the intersection of point and essential spectrum, such an ap proach had for a long time seemed out of reach. The stability problem for "in viscid" shock waves has been given a novel, clear and concise treatment by Guy Metivier and coworkers through the use of paradifferential calculus. The L 1 semi group theory for systems of conservation laws, itself still a recent development, has been considerably condensed by the introduction of new distance functionals through Tai-Ping Liu and collaborators; these functionals compare solutions to different data by direct reference to their wave structure. The fundamental prop erties of systems with relaxation have found a systematic description through the papers of Wen-An Yong; for shock waves, this means a first general theorem on the existence of corresponding profiles. The five articles of this book reflect the above developments.
