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Author : Alain Haraux
Publisher : Springer
Page : 324 pages
File Size : 46,9 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540385349
Author : Reinhard Racke
Publisher : Birkhäuser
Page : 306 pages
File Size : 50,9 Mb
Release : 2015-08-31
Category : Mathematics
ISBN : 9783319218731
This book mainly serves as an elementary, self-contained introduction to several important aspects of the theory of global solutions to initial value problems for nonlinear evolution equations. The book employs the classical method of continuation of local solutions with the help of a priori estimates obtained for small data. The existence and uniqueness of small, smooth solutions that are defined for all values of the time parameter are investigated. Moreover, the asymptotic behaviour of the solutions is described as time tends to infinity. The methods for nonlinear wave equations are discussed in detail. Other examples include the equations of elasticity, heat equations, the equations of thermoelasticity, Schrödinger equations, Klein-Gordon equations, Maxwell equations and plate equations. To emphasize the importance of studying the conditions under which small data problems offer global solutions, some blow-up results are briefly described. Moreover, the prospects for corresponding initial boundary value problems and for open questions are provided. In this second edition, initial-boundary value problems in waveguides are additionally considered.
Author : Songmu Zheng
Publisher : CRC Press
Page : 302 pages
File Size : 53,7 Mb
Release : 2004-07-08
Category : Mathematics
ISBN : 9781135436476
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 : Gaston M. N'Guerekata
Publisher : Nova Publishers
Page : 258 pages
File Size : 42,7 Mb
Release : 2008
Category : Mathematics
ISBN : 1604562269
This book presents high-quality research from around the world on the theory and methods of linear or nonlinear evolution equations as well as their further applications. Equations dealing with the asymptotic behavior of solutions to evolution equations are included. The book also covers degenerate parabolic equations, abstract differential equations, comments on the Schrodinger equation, solutions in banach spaces, periodic and quasi-periodic solutions, concave Lagragian systems and integral equations.
Author : Tatsien Li
Publisher : World Scientific
Page : 286 pages
File Size : 42,5 Mb
Release : 1997-01-04
Category : Electronic
ISBN : 9789814546423
This volume contains 30 research papers presenting the recent development and trend on the following subjects: nonlinear hyperbolic equations (systems); nonlinear parabolic equations (systems); infinite-dimensional dynamical systems; applications (free boundary problems, phase transitions, etc.).
Author : Songmu Zheng
Publisher : CRC Press
Page : 304 pages
File Size : 45,9 Mb
Release : 2004-07-08
Category : Mathematics
ISBN : 9780203492222
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
Author : Baoxiang Wang,Zhaohui Huo,Chengchun Hao,Zihua Guo
Publisher : World Scientific
Page : 298 pages
File Size : 41,9 Mb
Release : 2011
Category : Mathematics
ISBN : 9789814360746
1. Fourier multiplier, function space [symbol]. 1.1. Schwartz space, tempered distribution, Fourier transform. 1.2. Fourier multiplier on L[symbol]. 1.3. Dyadic decomposition, Besov and Triebel spaces. 1.4. Embeddings on X[symbol]. 1.5. Differential-difference norm on [symbol]. 1.6. Homogeneous space [symbol] 1.7. Bessel (Riesz) potential spaces [symbol]. 1.8. Fractional Gagliardo-Nirenberg inequalities -- 2. Navier-Stokes equation. 2.1. Introduction. 2.2. Time-space estimates for the heat semi-group. 2.3. Global well-posedness in L[symbol] of NS in 2D. 2.4. Well-posedness in L[symbol] of NS in higher dimensions. 2.5. Regularity of solutions for NS -- 3. Strichartz estimates for linear dispersive equations. 3.1. [symbol] estimates for the dispersive semi-group. 3.2. Strichartz inequalities : dual estimate techniques. 3.3. Strichartz estimates at endpoints -- 4. Local and global wellposedness for nonlinear dispersive equations. 4.1. Why is the Strichartz estimate useful. 4.2. Nonlinear mapping estimates in Besov spaces. 4.3. Critical and subcritical NLS in H[symbol]. 4.4. Global wellposedness of NLS in L[symbol] and H[symbol]. 4.5. Critical and subcritical NLKG in H[symbol]. 5. The low regularity theory for the nonlinear dispersive equations. 5.1. Bourgain space. 5.2. Local smoothing effect and maximal function estimates. 5.3. Bilinear estimates for KdV and local well-posedness. 5.4. Local well-posedness for KdV in H[symbol]. 5.5. I-method. 5.6. Schrodinger equation with derivative. 5.7. Some other dispersive equations -- 6. Frequency-uniform decomposition techniques. 6.1. Why does the frequency-uniform decomposition work. 6.2. Frequency-uniform decomposition, modulation spaces. 6.3. Inclusions between Besov and modulation spaces. 6.4. NLS and NLKG in modulation spaces. 6.5. Derivative nonlinear Schrodinger equations -- 7. Conservations, Morawetz' estimates of nonlinear Schrodinger equations. 7.1. Nother's theorem. 7.2. Invariance and conservation law. 7.3. Virial identity and Morawetz inequality. 7.4. Morawetz' interaction inequality. 7.5. Scattering results for NLS -- 8. Boltzmann equation without angular cutoff. 8.1. Models for collisions in kinetic theory. 8.2. Basic surgery tools for the Boltzmann operator. 8.3. Properties of Boltzmann collision operator without cutoff. 8.4 Regularity of solutions for spatially homogeneous case
Author : Nina B. Maslova
Publisher : World Scientific
Page : 210 pages
File Size : 53,8 Mb
Release : 1993
Category : Mathematics
ISBN : 9810211627
The book is devoted to the questions of the long-time behavior of solutions for evolution equations, connected with kinetic models in statistical physics. There is a wide variety of problems where such models are used to obtain reasonable physical as well as numerical results (Fluid Mechanics, Gas Dynamics, Plasma Physics, Nuclear Physics, Turbulence Theory etc.). The classical examples provide the nonlinear Boltzmann equation. Investigation of the long-time behavior of the solutions for the Boltzmann equation gives an approach to the nonlinear fluid dynamic equations. From the viewpoint of dynamical systems, the fluid dynamic equations arise in the theory as a tool to describe an attractor of the kinetic equation.
Author : Michael G. Crandall
Publisher : Elsevier
Page : 266 pages
File Size : 47,8 Mb
Release : 2014-05-10
Category : Mathematics
ISBN : 9781483269283
Nonlinear Evolution Equation covers the proceedings of the Symposium by the same title, conducted by the Mathematics Research Center at the University of Wisconsin, Madison on October 17-19, 1977. This book is divided into 13 chapters and begins with reviews of the uniqueness of solution to systems of conservation laws and the computational aspects of Glimm’s method. The next chapters examine the theoretical and practical aspects of Boltzmann, Navier-Stokes, and evolution equations. These topics are followed by discussions of the practical applications of Trotter’s product formula for some nonlinear semigroups and the finite time blow-up in nonlinear problems. The closing chapters deal with a Hamiltonian approach to the K-dV and other equations, along with a variational method for finding periodic solutions of differential equations. This book will prove useful to mathematicians and engineers.
Author : Gheorghe Morosanu
Publisher : Springer Science & Business Media
Page : 362 pages
File Size : 54,5 Mb
Release : 1988-08-31
Category : Science
ISBN : 9027724865
Author : Boling Guo,Fei Chen,Jing Shao,Ting Luo
Publisher : Walter de Gruyter GmbH & Co KG
Page : 346 pages
File Size : 49,6 Mb
Release : 2019-11-05
Category : Mathematics
ISBN : 9783110615470
Nonlinear Evolution Equation presents state-of-the-art theories and results on nonlinear evolution equation, showing related mathematical methods and applications. The basic concepts and research methods of infinite dimensional dynamical systems are discussed in detail. The unique combination of mathematical rigor and physical background makes this work an essential reference for researchers and students in applied mathematics and physics.
Author : Wolfgang Arendt,Haim Brezis,Michel Pierre
Publisher : Birkhäuser
Page : 803 pages
File Size : 55,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034879248
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 : Pavel Ivanovich Naumkin
Publisher : American Mathematical Soc.
Page : 312 pages
File Size : 42,6 Mb
Release : 2024-06-17
Category : Science
ISBN : 0821887696
This book is the first to concentrate on the theory of nonlinear nonlocal equations. The authors solve a number of problems concerning the asymptotic behavior of solutions of nonlinear evolution equations, the blow-up of solutions, and the global in time existence of solutions. In addition, a new classification of nonlinear nonlocal equations is introduced. A large class of these equations is treated by a single method, the main features of which are apriori estimates in different integral norms and use of the Fourier transform. This book will interest specialists in partial differential equations, as well as physicists and engineers.
Author : J. Kral
Publisher : Springer Science & Business Media
Page : 138 pages
File Size : 47,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461344254
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 : Tatsien Li,Piero De Mottoni
Publisher : World Scientific
Page : 274 pages
File Size : 49,9 Mb
Release : 1991-11-29
Category : Electronic
ISBN : 9789814569385
