Linear And Quasi Linear Evolution Equations In Hilbert Spaces

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Linear and Quasi-linear Evolution Equations in Hilbert Spaces

Author : Pascal Cherrier
Publisher : American Mathematical Society
ISBN 13 : 1470471442
Total Pages : 400 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Linear and Quasi-linear Evolution Equations in Hilbert Spaces by : Pascal Cherrier

Download or read book Linear and Quasi-linear Evolution Equations in Hilbert Spaces written by Pascal Cherrier and published by American Mathematical Society. This book was released on 2022-07-14 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book considers evolution equations of hyperbolic and parabolic type. These equations are studied from a common point of view, using elementary methods, such as that of energy estimates, which prove to be quite versatile. The authors emphasize the Cauchy problem and present a unified theory for the treatment of these equations. In particular, they provide local and global existence results, as well as strong well-posedness and asymptotic behavior results for the Cauchy problem for quasi-linear equations. Solutions of linear equations are constructed explicitly, using the Galerkin method; the linear theory is then applied to quasi-linear equations, by means of a linearization and fixed-point technique. The authors also compare hyperbolic and parabolic problems, both in terms of singular perturbations, on compact time intervals, and asymptotically, in terms of the diffusion phenomenon, with new results on decay estimates for strong solutions of homogeneous quasi-linear equations of each type. This textbook presents a valuable introduction to topics in the theory of evolution equations, suitable for advanced graduate students. The exposition is largely self-contained. The initial chapter reviews the essential material from functional analysis. New ideas are introduced along with their context. Proofs are detailed and carefully presented. The book concludes with a chapter on applications of the theory to Maxwell's equations and von Karman's equations.

Beyond Partial Differential Equations

Author : Horst Reinhard Beyer
Publisher : Springer
ISBN 13 : 3540711295
Total Pages : 291 pages
Book Rating : 4.5/5 (47 download)

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Book Synopsis Beyond Partial Differential Equations by : Horst Reinhard Beyer

Download or read book Beyond Partial Differential Equations written by Horst Reinhard Beyer and published by Springer. This book was released on 2007-04-10 with total page 291 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces the treatment of linear and nonlinear (quasi-linear) abstract evolution equations by methods from the theory of strongly continuous semigroups. The theoretical part is accessible to graduate students with basic knowledge in functional analysis, with only some examples requiring more specialized knowledge from the spectral theory of linear, self-adjoint operators in Hilbert spaces. Emphasis is placed on equations of the hyperbolic type which are less often treated in the literature.

SDE and BSDE on Hilbert Spaces

Author : Rongchan Zhu
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (17 download)

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Book Synopsis SDE and BSDE on Hilbert Spaces by : Rongchan Zhu

Download or read book SDE and BSDE on Hilbert Spaces written by Rongchan Zhu and published by . This book was released on 2012 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Nonlinear Evolution and Difference Equations of Monotone Type in Hilbert Spaces

Author : Behzad Djafari Rouhani
Publisher : CRC Press
ISBN 13 : 148222819X
Total Pages : 450 pages
Book Rating : 4.4/5 (822 download)

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Book Synopsis Nonlinear Evolution and Difference Equations of Monotone Type in Hilbert Spaces by : Behzad Djafari Rouhani

Download or read book Nonlinear Evolution and Difference Equations of Monotone Type in Hilbert Spaces written by Behzad Djafari Rouhani and published by CRC Press. This book was released on 2019-05-20 with total page 450 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Evolution Equations in Scales of Banach Spaces

Author : Oliver Caps
Publisher : Springer Science & Business Media
ISBN 13 : 3322800393
Total Pages : 310 pages
Book Rating : 4.3/5 (228 download)

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Book Synopsis Evolution Equations in Scales of Banach Spaces by : Oliver Caps

Download or read book Evolution Equations in Scales of Banach Spaces written by Oliver Caps and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book provides a new functional-analytic approach to evolution equations by considering the abstract Cauchy problem in a scale of Banach spaces. Conditions are proved characterizing well-posedness of the linear, time-dependent Cauchy problem in scales of Banach spaces and implying local existence, uniqueness, and regularity of solutions of the quasilinear Cauchy problem. Many applications illustrate the generality of the approach. In particular, using the Fefferman-Phong inequality unifying results on parabolic and hyperbolic equations generalizing classical ones and a unified treatment of Navier-Stokes and Euler equations is described. Assuming only basic knowledge in analysis and functional analysis the book provides all mathematical tools and is aimed for students, graduates, researchers, and lecturers.

Semilinear Evolution Equations and Their Applications

Author : Toka Diagana
Publisher : Springer
ISBN 13 : 303000449X
Total Pages : 199 pages
Book Rating : 4.0/5 (3 download)

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Book Synopsis Semilinear Evolution Equations and Their Applications by : Toka Diagana

Download or read book Semilinear Evolution Equations and Their Applications written by Toka Diagana and published by Springer. This book was released on 2018-10-23 with total page 199 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, which is a continuation of Almost Automorphic Type and Almost Periodic Type Functions in Abstract Spaces, presents recent trends and developments upon fractional, first, and second order semilinear difference and differential equations, including degenerate ones. Various stability, uniqueness, and existence results are established using various tools from nonlinear functional analysis and operator theory (such as semigroup methods). Various applications to partial differential equations and the dynamic of populations are amply discussed. This self-contained volume is primarily intended for advanced undergraduate and graduate students, post-graduates and researchers, but may also be of interest to non-mathematicians such as physicists and theoretically oriented engineers. It can also be used as a graduate text on evolution equations and difference equations and their applications to partial differential equations and practical problems arising in population dynamics. For completeness, detailed preliminary background on Banach and Hilbert spaces, operator theory, semigroups of operators, and almost periodic functions and their spectral theory are included as well.

Quasi-linear Evolution Equations in Non-reflexive Branch Spaces and Applications to Hyperbolic Systems

Author : Masaomi Nakata
Publisher :
ISBN 13 :
Total Pages : 168 pages
Book Rating : 4.:/5 (29 download)

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Book Synopsis Quasi-linear Evolution Equations in Non-reflexive Branch Spaces and Applications to Hyperbolic Systems by : Masaomi Nakata

Download or read book Quasi-linear Evolution Equations in Non-reflexive Branch Spaces and Applications to Hyperbolic Systems written by Masaomi Nakata and published by . This book was released on 1983 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Nonlinear Evolution Equations

Author : Nina Nikolaevna Uraltseva
Publisher : American Mathematical Soc.
ISBN 13 : 9780821895955
Total Pages : 240 pages
Book Rating : 4.8/5 (959 download)

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Book Synopsis Nonlinear Evolution Equations by : Nina Nikolaevna Uraltseva

Download or read book Nonlinear Evolution Equations written by Nina Nikolaevna Uraltseva and published by American Mathematical Soc.. This book was released on 1995-05-19 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection focuses on nonlinear problems in partial differential equations. Most of the papers are based on lectures presented at the seminar on partial differential equations and mathematical physics at St. Petersburg University. Among the topics explored are the existence and properties of solutions of various classes of nonlinear evolution equations, nonlinear imbedding theorems, bifurcations of solutions, and equations of mathematical physics (Navier-Stokes type equations and the nonlinear Schrodinger equation). The book will be useful to researchers and graduate students working in partial differential equations and mathematical physics.

Nonlinear Evolution Equations And Their Applications - Proceedings Of The Luso-chinese Symposium

Author : Tatsien Li
Publisher : World Scientific
ISBN 13 : 9814543446
Total Pages : 334 pages
Book Rating : 4.8/5 (145 download)

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Book Synopsis Nonlinear Evolution Equations And Their Applications - Proceedings Of The Luso-chinese Symposium by : Tatsien Li

Download or read book Nonlinear Evolution Equations And Their Applications - Proceedings Of The Luso-chinese Symposium written by Tatsien Li and published by World Scientific. This book was released on 1999-08-31 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Linear and Quasilinear Parabolic Problems

Author : Herbert Amann
Publisher : Birkhäuser
ISBN 13 : 3034892217
Total Pages : 366 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis Linear and Quasilinear Parabolic Problems by : Herbert Amann

Download or read book Linear and Quasilinear Parabolic Problems written by Herbert Amann and published by Birkhäuser. This book was released on 2012-12-06 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this treatise we present the semigroup approach to quasilinear evolution equa of parabolic type that has been developed over the last ten years, approxi tions mately. It emphasizes the dynamic viewpoint and is sufficiently general and flexible to encompass a great variety of concrete systems of partial differential equations occurring in science, some of those being of rather 'nonstandard' type. In partic ular, to date it is the only general method that applies to noncoercive systems. Although we are interested in nonlinear problems, our method is based on the theory of linear holomorphic semigroups. This distinguishes it from the theory of nonlinear contraction semigroups whose basis is a nonlinear version of the Hille Yosida theorem: the Crandall-Liggett theorem. The latter theory is well-known and well-documented in the literature. Even though it is a powerful technique having found many applications, it is limited in its scope by the fact that, in concrete applications, it is closely tied to the maximum principle. Thus the theory of nonlinear contraction semigroups does not apply to systems, in general, since they do not allow for a maximum principle. For these reasons we do not include that theory.

Evolution Equations And Approximations

Author : Kazufumi Ito
Publisher : World Scientific
ISBN 13 : 9814488380
Total Pages : 518 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Evolution Equations And Approximations by : Kazufumi Ito

Download or read book Evolution Equations And Approximations written by Kazufumi Ito and published by World Scientific. This book was released on 2002-05-24 with total page 518 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents an approximation theory for a general class of nonlinear evolution equations in Banach spaces and the semigroup theory, including the linear (Hille-Yosida), nonlinear (Crandall-Liggett) and time-dependent (Crandall-Pazy) theorems.The implicit finite difference method of Euler is shown to generate a sequence convergent to the unique integral solution of evolution equations of the maximal monotone type. Moreover, the Chernoff theory provides a sufficient condition for consistent and stable time integration of time-dependent nonlinear equations. The Trotter-Kato theorem and the Lie-Trotter type product formula give a mathematical framework for the convergence analysis of numerical approximations of solutions to a general class of partial differential equations. This book contains examples demonstrating the applicability of the generation as well as the approximation theory.In addition, the Kobayashi-Oharu approach of locally quasi-dissipative operators is discussed for homogeneous as well as nonhomogeneous equations. Applications to the delay differential equations, Navier-Stokes equation and scalar conservation equation are given.

Nonlinear Evolution Equations and Potential Theory

Author : J. Kral
Publisher : Springer Science & Business Media
ISBN 13 : 1461344255
Total Pages : 138 pages
Book Rating : 4.4/5 (613 download)

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Book Synopsis Nonlinear Evolution Equations and Potential Theory by : J. Kral

Download or read book Nonlinear Evolution Equations and Potential Theory written by J. Kral and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Quasi-linear Evolution Equations in Non-reflexive Banach Spaces and Applications to Hyperbolic Systems

Author : Masaomi Nakata
Publisher :
ISBN 13 :
Total Pages : 77 pages
Book Rating : 4.:/5 (494 download)

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Book Synopsis Quasi-linear Evolution Equations in Non-reflexive Banach Spaces and Applications to Hyperbolic Systems by : Masaomi Nakata

Download or read book Quasi-linear Evolution Equations in Non-reflexive Banach Spaces and Applications to Hyperbolic Systems written by Masaomi Nakata and published by . This book was released on 1983 with total page 77 pages. Available in PDF, EPUB and Kindle. Book excerpt:

An Introduction to Semilinear Evolution Equations

Author : Thierry Cazenave
Publisher : Oxford University Press
ISBN 13 : 9780198502777
Total Pages : 204 pages
Book Rating : 4.5/5 (27 download)

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Book Synopsis An Introduction to Semilinear Evolution Equations by : Thierry Cazenave

Download or read book An Introduction to Semilinear Evolution Equations written by Thierry Cazenave and published by Oxford University Press. This book was released on 1998 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents in a self-contained form the typical basic properties of solutions to semilinear evolutionary partial differential equations, with special emphasis on global properties. It has a didactic ambition and will be useful for an applied readership as well as theoretical researchers.

Recent Trends In Differential Equations

Author : Ravi P Agarwal
Publisher : World Scientific
ISBN 13 : 9814505625
Total Pages : 601 pages
Book Rating : 4.8/5 (145 download)

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Book Synopsis Recent Trends In Differential Equations by : Ravi P Agarwal

Download or read book Recent Trends In Differential Equations written by Ravi P Agarwal and published by World Scientific. This book was released on 1992-05-07 with total page 601 pages. Available in PDF, EPUB and Kindle. Book excerpt: This series aims at reporting new developments of a high mathematical standard and of current interest. Each volume in the series shall be devoted to mathematical analysis that has been applied, or potentially applicable to the solutions of scientific, engineering, and social problems. The first volume of WSSIAA contains 42 research articles on differential equations by leading mathematicians from all over the world. This volume has been dedicated to V Lakshmikantham on his 65th birthday for his significant contributions in the field of differential equations.

Handbook of Differential Equations: Evolutionary Equations

Author : C.M. Dafermos
Publisher : Elsevier
ISBN 13 : 0080521827
Total Pages : 579 pages
Book Rating : 4.0/5 (85 download)

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Book Synopsis Handbook of Differential Equations: Evolutionary Equations by : C.M. Dafermos

Download or read book Handbook of Differential Equations: Evolutionary Equations written by C.M. Dafermos and published by Elsevier. This book was released on 2004-08-24 with total page 579 pages. Available in PDF, EPUB and Kindle. Book excerpt: This 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. The table of contents includes: W.Arendt: Semigroups and evolution equations: Calculus, regularity and kernel estimates A.Bressan: The front tracking method for systems of conservation laws E.DiBenedetto, J.M.Urbano,V.Vespri: Current issues on singular and degenerate evolution equations; L.Hsiao, S.Jiang: Nonlinear hyperbolic-parabolic coupled systems A.Lunardi: Nonlinear parabolic equations and systems D.Serre:L1-stability of nonlinear waves in scalar conservation laws B.Perthame:Kinetic formulations of parabolic and hyperbolic PDE’s: from theory to numerics

Boundary Value Problems for Linear Evolution Partial Differential Equations

Author : H.G. Garnir
Publisher : Springer Science & Business Media
ISBN 13 : 9401012059
Total Pages : 484 pages
Book Rating : 4.4/5 (1 download)

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Book Synopsis Boundary Value Problems for Linear Evolution Partial Differential Equations by : H.G. Garnir

Download or read book Boundary Value Problems for Linear Evolution Partial Differential Equations written by H.G. Garnir and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 484 pages. Available in PDF, EPUB and Kindle. Book excerpt: Most of the problems posed by Physics to Mathematical Analysis are boundary value problems for partial differential equations and systems. Among them, the problems concerning linear evolution equations have an outstanding position in the study of the physical world, namely in fluid dynamics, elastodynamics, electromagnetism, plasma physics and so on. This Institute was devoted to these problems. It developed essentially the new methods inspired by Functional Analysis and specially by the theories of Hilbert spaces, distributions and ultradistributions. The lectures brought a detailed exposition of the novelties in this field by world known specialists. We held the Institute at the Sart Tilman Campus of the University of Liege from September 6 to 17, 1976. It was attended by 99 participants, 79 from NATO Countries [Belgium (30), Canada (2), Denmark (I), France (15), West Germany (9), Italy (5), Turkey (3), USA (14)] and 20 from non NATO Countries [Algeria (2), Australia (3), Austria (I), Finland (1), Iran (3), Ireland (I), Japan (6), Poland (1), Sweden (I), Zair (1)]. There were 5 courses of_ 6_ h. ollI'. s~. 1. nL lJ. , h. t;l. l. I. rl"~, 1. n,L ,_ h. t;l. l. I. r. !'~ , ?_ n. f~ ?_ h,,