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 : 4.46/5 ( download)

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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.

Author : Horst Reinhard Beyer
Publisher : Springer
ISBN 13 : 3540711295
Total Pages : 291 pages
Book Rating : 4.92/5 ( download)

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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.

Author : Behzad Djafari Rouhani
Publisher : CRC Press
ISBN 13 : 148222819X
Total Pages : 450 pages
Book Rating : 4.99/5 ( download)

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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.

Author : Oliver Caps
Publisher : Springer Science & Business Media
ISBN 13 : 3322800393
Total Pages : 310 pages
Book Rating : 4.98/5 ( download)

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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.

Author : Giuseppe Da Prato
Publisher : Cambridge University Press
ISBN 13 : 1139433431
Total Pages : 397 pages
Book Rating : 4.33/5 ( download)

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Download or read book Second Order Partial Differential Equations in Hilbert Spaces written by Giuseppe Da Prato and published by Cambridge University Press. This book was released on 2002-07-25 with total page 397 pages. Available in PDF, EPUB and Kindle. Book excerpt: State of the art treatment of a subject which has applications in mathematical physics, biology and finance. Includes discussion of applications to control theory. There are numerous notes and references that point to further reading. Coverage of some essential background material helps to make the book self contained.

Author : Toka Diagana
Publisher : Springer
ISBN 13 : 303000449X
Total Pages : 189 pages
Book Rating : 4.91/5 ( download)

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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 189 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.

Author : Nina Nikolaevna Uraltseva
Publisher : American Mathematical Soc.
ISBN 13 : 9780821895955
Total Pages : 240 pages
Book Rating : 4.58/5 ( download)

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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.

Author : Herbert Amann
Publisher : Birkhäuser
ISBN 13 : 3034892217
Total Pages : 366 pages
Book Rating : 4.16/5 ( download)

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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.

Author : Jan Prüss
Publisher : Birkhäuser
ISBN 13 : 3319276980
Total Pages : 609 pages
Book Rating : 4.84/5 ( download)

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Download or read book Moving Interfaces and Quasilinear Parabolic Evolution Equations written by Jan Prüss and published by Birkhäuser. This book was released on 2016-07-25 with total page 609 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this monograph, the authors develop a comprehensive approach for the mathematical analysis of a wide array of problems involving moving interfaces. It includes an in-depth study of abstract quasilinear parabolic evolution equations, elliptic and parabolic boundary value problems, transmission problems, one- and two-phase Stokes problems, and the equations of incompressible viscous one- and two-phase fluid flows. The theory of maximal regularity, an essential element, is also fully developed. The authors present a modern approach based on powerful tools in classical analysis, functional analysis, and vector-valued harmonic analysis. The theory is applied to problems in two-phase fluid dynamics and phase transitions, one-phase generalized Newtonian fluids, nematic liquid crystal flows, Maxwell-Stefan diffusion, and a variety of geometric evolution equations. The book also includes a discussion of the underlying physical and thermodynamic principles governing the equations of fluid flows and phase transitions, and an exposition of the geometry of moving hypersurfaces.

Author : J. Kral
Publisher : Springer Science & Business Media
ISBN 13 : 1461344255
Total Pages : 138 pages
Book Rating : 4.54/5 ( download)

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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.