Nonlinear Evolution Equations And Potential Theory
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Nonlinear Evolution Equations And Potential Theory
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Author : J. Kral
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Nonlinear Evolution Equations And Potential Theory written by J. Kral and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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.
Nonlinear Evolution Equations And Potential Theory
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Author : J. Kral
language : en
Publisher:
Release Date : 1975-04-01
Nonlinear Evolution Equations And Potential Theory written by J. Kral and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1975-04-01 with categories.
Nonlinear Evolution Equations And Potential Theory
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Author : J. Kral
language : en
Publisher: Springer
Release Date : 1975-04-01
Nonlinear Evolution Equations And Potential Theory written by J. Kral and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1975-04-01 with Mathematics categories.
Harmonic Analysis Method For Nonlinear Evolution Equations I
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Author : Baoxiang Wang
language : en
Publisher: World Scientific
Release Date : 2011
Harmonic Analysis Method For Nonlinear Evolution Equations I written by Baoxiang Wang and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Mathematics categories.
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
Nonlinear Evolution Equations And Dynamical Systems
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Author : Sandra Carillo
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Nonlinear Evolution Equations And Dynamical Systems written by Sandra Carillo and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
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.
Lectures On Nonlinear Evolution Equations
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Author : Reinhard Racke
language : en
Publisher: Birkhäuser
Release Date : 2015-08-31
Lectures On Nonlinear Evolution Equations written by Reinhard Racke and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-08-31 with Mathematics categories.
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.
Measure Theory And Nonlinear Evolution Equations
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Author : Flavia Smarrazzo
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2022-04-19
Measure Theory And Nonlinear Evolution Equations written by Flavia Smarrazzo and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-04-19 with Mathematics categories.
This carefully written text on measure theory with applications to partial differential equations covers general measure theory, Lebesgue spaces of real-valued and vector-valued functions, different notions of measurability for the latter, weak convergence of functions and measures, Radon and Young measures, capacity, and finally applications to quasilinear parabolic problems (in particular, forward-backward equations).
Nonlinear Evolution Equations
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Author : Songmu Zheng
language : en
Publisher: CRC Press
Release Date : 2004-07-08
Nonlinear Evolution Equations written by Songmu Zheng and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-07-08 with Mathematics categories.
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.
Nonlinear Evolution Equations Solvable By The Spectral Transform
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Author : F. Calogero
language : en
Publisher: Pitman Publishing
Release Date : 1978
Nonlinear Evolution Equations Solvable By The Spectral Transform written by F. Calogero and has been published by Pitman Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 1978 with Mathematics categories.
The volume contains the text of the invited lectures presented at the International Symposium on "Nonlinear Evolution Equations Solvable by the Inverse Spectral Transform", that took place at the Accademia dei Lincei in Rome from June 15 through June 18, 1977. It introduces an important mathematical technique based on the spectral transform and relevant to the solution of nonlinear evolution equations. These texts will be of particular value to theoretical physicists (in plasma, nonlinear optics, hydrodynamics, solid state and elementary particles); applied mathematicians interested in nonlinear evolution equations; and pure mathematicians interested in algebraic and differential geometry.
Loop Like Solitons In The Theory Of Nonlinear Evolution Equations
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Author : V. O. Vakhnenko
language : en
Publisher: Cambridge Scholars Publishing
Release Date : 2022-02-17
Loop Like Solitons In The Theory Of Nonlinear Evolution Equations written by V. O. Vakhnenko and has been published by Cambridge Scholars Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-02-17 with Science categories.
This book shows that the physical phenomena and processes that take place in nature generally have complicated nonlinear features, which leads to nonlinear mathematical models for the real processes. It focuses on the practical issues involved here, as well as the development of methods to investigate the associated nonlinear mathematical problems, including nonlinear wave propagation. It acquaints the reader with a series of methods and approaches that can be applied to a wide class of nonlinear equations. The book also outlines a way in which an uninitiated reader could investigate a new nonlinear equation.