Measure Theory And Nonlinear Evolution Equations

Author : Flavia Smarrazzo,Alberto Tesei
Publisher : Walter de Gruyter GmbH & Co KG
Page : 456 pages
File Size : 55,8 Mb
Release : 2022-04-19
Category : Mathematics
ISBN : 9783110556902

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Measure Theory and Nonlinear Evolution Equations by Flavia Smarrazzo,Alberto Tesei Pdf

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).

Author : J. Kral
Publisher : Springer Science & Business Media
Page : 138 pages
File Size : 53,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461344254

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Nonlinear Evolution Equations and Potential Theory by J. Kral Pdf

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 : Wolfgang Arendt,Haim Brezis,Michel Pierre
Publisher : Birkhäuser
Page : 803 pages
File Size : 41,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034879248

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Nonlinear Evolution Equations and Related Topics by Wolfgang Arendt,Haim Brezis,Michel Pierre Pdf

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 : Reinhard Racke
Publisher : Birkhäuser
Page : 306 pages
File Size : 53,5 Mb
Release : 2015-08-31
Category : Mathematics
ISBN : 9783319218731

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Lectures on Nonlinear Evolution Equations by Reinhard Racke Pdf

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 : Baoxiang Wang,Zhaohui Huo,Chengchun Hao,Zihua Guo
Publisher : World Scientific
Page : 298 pages
File Size : 42,8 Mb
Release : 2011
Category : Mathematics
ISBN : 9789814360746

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Harmonic Analysis Method for Nonlinear Evolution Equations, I by Baoxiang Wang,Zhaohui Huo,Chengchun Hao,Zihua Guo Pdf

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 : Alain Haraux
Publisher : Springer
Page : 324 pages
File Size : 51,5 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540385349

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Nonlinear Evolution Equations - Global Behavior of Solutions by Alain Haraux Pdf

Author : N. U. Ahmed,Shian Wang
Publisher : Springer Nature
Page : 236 pages
File Size : 50,8 Mb
Release : 2023-09-12
Category : Mathematics
ISBN : 9783031372605

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Measure-Valued Solutions for Nonlinear Evolution Equations on Banach Spaces and Their Optimal Control by N. U. Ahmed,Shian Wang Pdf

This book offers the first comprehensive presentation of measure-valued solutions for nonlinear deterministic and stochastic evolution equations on infinite dimensional Banach spaces. Unlike traditional solutions, measure-valued solutions allow for a much broader class of abstract evolution equations to be addressed, providing a broader approach. The book presents extensive results on the existence of measure-valued solutions for differential equations that have no solutions in the usual sense. It covers a range of topics, including evolution equations with continuous/discontinuous vector fields, neutral evolution equations subject to vector measures as impulsive forces, stochastic evolution equations, and optimal control of evolution equations. The optimal control problems considered cover the existence of solutions, necessary conditions of optimality, and more, significantly complementing the existing literature. This book will be of great interest to researchers in functional analysis, partial differential equations, dynamic systems and their optimal control, and their applications, advancing previous research and providing a foundation for further exploration of the field.

Author : Barbara L. Keyfitz,Michael Shearer
Publisher : Springer Science & Business Media
Page : 297 pages
File Size : 53,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461390497

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Nonlinear Evolution Equations That Change Type by Barbara L. Keyfitz,Michael Shearer Pdf

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 : Nicolae H. Pavel
Publisher : Springer
Page : 292 pages
File Size : 41,6 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540471868

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Nonlinear Evolution Operators and Semigroups by Nicolae H. Pavel Pdf

This research monograph deals with nonlinear evolution operators and semigroups generated by dissipative (accretive), possibly multivalued operators, as well as with the application of this theory to partial differential equations. It shows that a large class of PDE's can be studied via the semigroup approach. This theory is not available otherwise in the self-contained form provided by these Notes and moreover a considerable part of the results, proofs and methods are not to be found in other books. The exponential formula of Crandall and Liggett, some simple estimates due to Kobayashi and others, the characterization of compact semigroups due to Brézis, the proof of a fundamental property due to Ursescu and the author and some applications to PDE are of particular interest. Assuming only basic knowledge of functional analysis, the book will be of interest to researchers and graduate students in nonlinear analysis and PDE, and to mathematical physicists.

Author : Gheorghe Morosanu
Publisher : Springer Science & Business Media
Page : 362 pages
File Size : 43,8 Mb
Release : 1988-08-31
Category : Science
ISBN : 9027724865

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Nonlinear Evolution Equations and Applications by Gheorghe Morosanu Pdf

Author : Songmu Zheng
Publisher : CRC Press
Page : 304 pages
File Size : 54,9 Mb
Release : 2004-07-08
Category : Mathematics
ISBN : 9780203492222

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Nonlinear Evolution Equations by Songmu Zheng Pdf

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 : Yi Cheng,Sen Hu,Yishen Li,Chia-kuei Peng
Publisher : World Scientific
Page : 204 pages
File Size : 54,5 Mb
Release : 2003-10-14
Category : Mathematics
ISBN : 9789814486644

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Nonlinear Evolution Equations And Dynamical Systems, Proceedings Of The Icm2002 Satellite Conference by Yi Cheng,Sen Hu,Yishen Li,Chia-kuei Peng Pdf

This book contains the papers presented at the ICM2002 Satellite Conference on Nonlinear Evolution Equations and Dynamical Systems. About 50 mathematicians and scientists attended the meeting — including E Witten (IAS), C Nappi (Princeton), K Khanin (Cambridge), D Phong (Columbia), d'Hoker (UCLA) and Peng Chiakuei (CAS). The book covers several fields, such as nonlinear evolution equations and integrable systems, infinite-dimensional algebra, conformal field theory and geometry.The proceedings have been selected for coverage in:• Index to Scientific & Technical Proceedings (ISTP CDROM version / ISI Proceedings)

Author : J. Necas,J. Malek,M. Rokyta,M. Ruzicka
Publisher : CRC Press
Page : 334 pages
File Size : 41,8 Mb
Release : 2019-08-16
Category : Mathematics
ISBN : 9781000723120

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Weak and Measure-Valued Solutions to Evolutionary PDEs by J. Necas,J. Malek,M. Rokyta,M. Ruzicka Pdf

This book provides a concise treatment of the theory of nonlinear evolutionary partial differential equations. It provides a rigorous analysis of non-Newtonian fluids, and outlines its results for applications in physics, biology, and mechanical engineering

Author : Boris L. Rozovsky,Sergey V. Lototsky
Publisher : Springer
Page : 330 pages
File Size : 51,5 Mb
Release : 2018-10-03
Category : Mathematics
ISBN : 9783319948935

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Stochastic Evolution Systems by Boris L. Rozovsky,Sergey V. Lototsky Pdf

This monograph, now in a thoroughly revised second edition, develops the theory of stochastic calculus in Hilbert spaces and applies the results to the study of generalized solutions of stochastic parabolic equations. The emphasis lies on second-order stochastic parabolic equations and their connection to random dynamical systems. The authors further explore applications to the theory of optimal non-linear filtering, prediction, and smoothing of partially observed diffusion processes. The new edition now also includes a chapter on chaos expansion for linear stochastic evolution systems. This book will appeal to anyone working in disciplines that require tools from stochastic analysis and PDEs, including pure mathematics, financial mathematics, engineering and physics.

Author : C.M. Dafermos,Eduard Feireisl
Publisher : Elsevier
Page : 652 pages
File Size : 40,5 Mb
Release : 2011-09-22
Category : Mathematics
ISBN : 008046565X

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Handbook of Differential Equations: Evolutionary Equations by C.M. Dafermos,Eduard Feireisl Pdf

The material collected in this volume reflects the active present of this area of mathematics, ranging from the abstract theory of gradient flows to stochastic representations of non-linear parabolic PDE's. Articles will highlight the present as well as expected future directions of development of the field with particular emphasis on applications. The article by Ambrosio and Savaré discusses the most recent development in the theory of gradient flow of probability measures. After an introduction reviewing the properties of the Wasserstein space and corresponding subdifferential calculus, applications are given to evolutionary partial differential equations. The contribution of Herrero provides a description of some mathematical approaches developed to account for quantitative as well as qualitative aspects of chemotaxis. Particular attention is paid to the limits of cell's capability to measure external cues on the one hand, and to provide an overall description of aggregation models for the slim mold Dictyostelium discoideum on the other. The chapter written by Masmoudi deals with a rather different topic - examples of singular limits in hydrodynamics. This is nowadays a well-studied issue given the amount of new results based on the development of the existence theory for rather general systems of equations in hydrodynamics. The paper by DeLellis addreses the most recent results for the transport equations with regard to possible applications in the theory of hyperbolic systems of conservation laws. Emphasis is put on the development of the theory in the case when the governing field is only a BV function. The chapter by Rein represents a comprehensive survey of results on the Poisson-Vlasov system in astrophysics. The question of global stability of steady states is addressed in detail. The contribution of Soner is devoted to different representations of non-linear parabolic equations in terms of Markov processes. After a brief introduction on the linear theory, a class of non-linear equations is investigated, with applications to stochastic control and differential games. The chapter written by Zuazua presents some of the recent progresses done on the problem of controllabilty of partial differential equations. The applications include the linear wave and heat equations,parabolic equations with coefficients of low regularity, and some fluid-structure interaction models. - Volume 1 focuses on the abstract theory of evolution - Volume 2 considers more concrete probelms relating to specific applications - Volume 3 reflects the active present of this area of mathematics, ranging from the abstract theory of gradient flows to stochastic representations of non-linear PDEs