Nonlinear Evolution Equations That Change Type
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Author | : Barbara L. Keyfitz |
Publisher | : Springer Science & Business Media |
Total Pages | : 297 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1461390494 |
This IMA Volume in Mathematics and its Applications NONLINEAR EVOLUTION EQUATIONS THAT CHANGE TYPE is based on the proceedings of a workshop which was an integral part of the 1988-89 IMA program on NONLINEAR WAVES. The workshop focussed on prob lems of ill-posedness and change of type which arise in modeling flows in porous materials, viscoelastic fluids and solids and phase changes. We thank the Coordinat ing Committee: James Glimm, Daniel Joseph, Barbara Lee Keyfitz, Andrew Majda, Alan Newell, Peter Olver, David Sattinger and David Schaeffer for planning and implementing an exciting and stimulating year-long program. We especially thank the workshop organizers, Barbara Lee Keyfitz and Michael Shearer, for their efforts in bringing together many of the major figures in those research fields in which theories for nonlinear evolution equations that change type are being developed. A vner Friedman Willard Miller, J r. ix PREFACE During the winter and spring quarters of the 1988/89 IMA Program on Non linear Waves, the issue of change of type in nonlinear partial differential equations appeared frequently. Discussion began with the January 1989 workshop on Two Phase Waves in Fluidized Beds, Sedimentation and Granular Flow; some of the papers in the proceedings of that workshop present strategies designed to avoid the appearance of change of type in models for multiphase fluid flow.
Author | : Songmu Zheng |
Publisher | : CRC Press |
Total Pages | : 302 |
Release | : 2004-07-08 |
Genre | : Mathematics |
ISBN | : 1135436479 |
Nonlinear evolution equations arise in many fields of sciences including physics, mechanics, and material science. This book introduces some important methods for dealing with these equations and explains clearly and concisely a wide range of relevant theories and techniques. These include the semigroup method, the compactness and monotone operator methods, the monotone iterative method and invariant regions, the global existence and uniqueness theory for small initial data, and the asymptotic behavior of solutions and global attractors. Many of the results are published in book form for the first time. Bibliographic comments in each chapter provide the reader with references and further reading materials to enable further research and study.
Author | : Behzad Djafari Rouhani |
Publisher | : CRC Press |
Total Pages | : 131 |
Release | : 2019-05-20 |
Genre | : Mathematics |
ISBN | : 0429528884 |
This book is devoted to the study of non-linear evolution and difference equations of first or second order governed by maximal monotone operator. This class of abstract evolution equations contains ordinary differential equations, as well as the unification of some important partial differential equations including heat equation, wave equation, Schrodinger equation, etc. The book contains a collection of the authors' work and applications in this field, as well as those of other authors.
Author | : J. Kral |
Publisher | : Springer Science & Business Media |
Total Pages | : 138 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1461344255 |
Preface.- Gottfried Anger: Direct and inverse problems in potential theory.- Viorel Barbu: Regularity results for sane differential equations associated with maximal monotone operators in Hilbert spaces.- Haim Brezis: Classes d'interpolation associées à un opérateur monotone et applications.- Siegfried Dnümmel: On inverse problems for k-dimensional potentials.- Jozef Ka?ur: Application of Rothe's method to nonlinear parabolic boundary value problems.- Josef Král: Potentials and removability of singularities.- Vladimir Lovicar: Theorem of Fréchet and asymptotically almost periodid solutions of.
Author | : Alain Haraux |
Publisher | : Springer |
Total Pages | : 324 |
Release | : 2006-11-15 |
Genre | : Mathematics |
ISBN | : 3540385347 |
Author | : Reinhard Racke |
Publisher | : Springer Science & Business Media |
Total Pages | : 268 |
Release | : 2013-06-29 |
Genre | : Mathematics |
ISBN | : 3663106292 |
This book serves as an elementary, self contained introduction into some important aspects of the theory of global solutions to initial value problems for nonlinear evolution equations. The presentation is made using the classical method of continuation of local solutions with the help of a priori estimates obtained for small data.
Author | : Tatsien Li |
Publisher | : World Scientific |
Total Pages | : 334 |
Release | : 1999-08-31 |
Genre | : |
ISBN | : 9814543446 |
This book discusses recent trends and developments in the area of nonlinear evolution equations. It is a collection of invited lectures on the following topics: nonlinear parabolic equations (systems); nonlinear hyperbolic systems; free boundary problems; conservation laws and shock waves; travelling and solitary waves; regularity, stability and singularity, etc.
Author | : Sandra Carillo |
Publisher | : Springer Science & Business Media |
Total Pages | : 247 |
Release | : 2012-12-06 |
Genre | : Science |
ISBN | : 3642840396 |
Nonlinear Evolution Equations and Dynamical Systems (NEEDS) provides a presentation of the state of the art. Except for a few review papers, the 40 contributions are intentially brief to give only the gist of the methods, proofs, etc. including references to the relevant litera- ture. This gives a handy overview of current research activities. Hence, the book should be equally useful to the senior resercher as well as the colleague just entering the field. Keypoints treated are: i) integrable systems in multidimensions and associated phenomenology ("dromions"); ii) criteria and tests of integrability (e.g., Painlev test); iii) new developments related to the scattering transform; iv) algebraic approaches to integrable systems and Hamiltonian theory (e.g., connections with Young-Baxter equations and Kac-Moody algebras); v) new developments in mappings and cellular automata, vi) applications to general relativity, condensed matter physics, and oceanography.
Author | : Wolfgang Arendt |
Publisher | : Springer Science & Business Media |
Total Pages | : 844 |
Release | : 2004-08-20 |
Genre | : Mathematics |
ISBN | : 9783764371074 |
Philippe Bénilan was a most original and charismatic mathematician who had a deep and decisive impact on the theory of Nonlinear Evolution Equations. Dedicated to him, Nonlinear Evolution Equations and Related Topics contains research papers written by highly distinguished mathematicians. They are all related to Philippe Benilan's work and reflect the present state of this most active field. The contributions cover a wide range of nonlinear and linear equations.
Author | : I︠U︡riĭ Alekseevich Mitropolʹskiĭ |
Publisher | : Springer Science & Business Media |
Total Pages | : 300 |
Release | : 1993 |
Genre | : Mathematics |
ISBN | : 9780792320548 |
Many problems in celestial mechanics, physics and engineering involve the study of oscillating systems governed by nonlinear ordinary differential equations or partial differential equations. This volume represents an important contribution to the available methods of solution for such systems.