Author: Viorel Barbu Publisher: Springer Science & Business Media ISBN: 1441955429 Category : Mathematics Languages : en Pages : 283
Book Description
This monograph is concerned with the basic results on Cauchy problems associated with nonlinear monotone operators in Banach spaces with applications to partial differential equations of evolutive type. It focuses on major results in recent decades.
Author: Giovanni Dore Publisher: CRC Press ISBN: 9780824790677 Category : Mathematics Languages : en Pages : 290
Book Description
This reference - based on the Conference on Differential Equations, held in Bologna - provides information on current research in parabolic and hyperbolic differential equations. Presenting methods and results in semigroup theory and their applications to evolution equations, this book focuses on topics including: abstract parabolic and hyperbolic linear differential equations; nonlinear abstract parabolic equations; holomorphic semigroups; and Volterra operator integral equations.;With contributions from international experts, Differential Equations in Banach Spaces is intended for research mathematicians in functional analysis, partial differential equations, operator theory and control theory; and students in these disciplines.
Author: Angelo Favini Publisher: CRC Press ISBN: 9780824716776 Category : Mathematics Languages : en Pages : 338
Book Description
This work presents a detailed study of linear abstract degenerate differential equations, using both the semigroups generated by multivalued (linear) operators and extensions of the operational method from Da Prato and Grisvard. The authors describe the recent and original results on PDEs and algebraic-differential equations, and establishes the analyzability of the semigroup generated by some degenerate parabolic operators in spaces of continuous functions.
Author: KREIN Publisher: Springer Science & Business Media ISBN: 1468480685 Category : Mathematics Languages : en Pages : 112
Book Description
INTRODUCTION . . . . . . xiii § 1. LINEAR EQUATIONS. BASIC NOTIONS . 3 § 2. EQUATIONS WITH A CLOSED OPERATOR 6 § 3. THE ADJOINT EQUATION . . . . . . 10 § 4. THE EQUATION ADJOINT TO THE FACTORED EQUATION. 17 § 5. AN EQUATION WITH A CLOSED OPERATOR WHICH HAS A DENSE DOMAIN 18 NORMALLY SOLVABLE EQUATIONS WITH FINITE DIMENSIONAL KERNEL. 22 § 6. A PRIORI ESTIMATES .. . . . . . 24 § 7. EQUATIONS WITH FINITE DEFECT . . . 27 § 8. § 9. SOME DIFFERENT ADJOINT EQUATIONS . 30 § 10. LINEAR TRANSFORMATIONS OF EQUATIONS 33 TRANSFORMATIONS OF d-NORMAL EQUATIONS . 38 § 11. § 12. NOETHERIAN EQUATIONS. INDEX. . . . . . 42 § 13. EQUATIONS WITH OPERATORS WHICH ACT IN A SINGLE SPACE 44 § 14. FREDHOLM EQUATIONS. REGULARIZATION OF EQUATIONS 46 § 15. LINEAR CHANGES OF VARIABLE . . . . . . . . 50 § 16. STABILITY OF THE PROPERTIES OF AN EQUATION 53 OVERDETERMINED EQUATIONS 59 § 17. § 18. UNDETERMINED EQUATIONS 62 § 19. INTEGRAL EQUATIONS . . . 65 DIFFERENTIAL EQUATIONS . 80 § 20. APPENDIX. BASIC RESULTS FROM FUNCTIONAL ANALYSIS USED IN THE TEXT 95 LITERATURE CITED . . . . . . . . . . . . . . . . . . .. . . . 99 . . PRE F ACE The basic material appearing in this book represents the substance v of a special series of lectures given by the author at Voronez University in 1968/69, and, in part, at Dagestan University in 1970.
Author: Giovanni Dore Publisher: CRC Press ISBN: 1000117103 Category : Mathematics Languages : en Pages : 289
Book Description
This reference - based on the Conference on Differential Equations, held in Bologna - provides information on current research in parabolic and hyperbolic differential equations. Presenting methods and results in semigroup theory and their applications to evolution equations, this book focuses on topics including: abstract parabolic and hyperbolic linear differential equations; nonlinear abstract parabolic equations; holomorphic semigroups; and Volterra operator integral equations.;With contributions from international experts, Differential Equations in Banach Spaces is intended for research mathematicians in functional analysis, partial differential equations, operator theory and control theory; and students in these disciplines.
Author: Gisele Ruiz Goldstein Publisher: CRC Press ISBN: 9780824709754 Category : Mathematics Languages : en Pages : 442
Book Description
Celebrating the work of renowned mathematician Jerome A. Goldstein, this reference compiles original research on the theory and application of evolution equations to stochastics, physics, engineering, biology, and finance. The text explores a wide range of topics in linear and nonlinear semigroup theory, operator theory, functional analysis, and linear and nonlinear partial differential equations, and studies the latest theoretical developments and uses of evolution equations in a variety of disciplines. Providing nearly 500 references, the book contains discussions by renowned mathematicians such as H. Brezis, G. Da Prato, N.E. Gretskij, I. Lasiecka, Peter Lax, M. M. Rao, and R. Triggiani.
Author: Alexander Tolstonogov Publisher: Springer Science & Business Media ISBN: 9780792366188 Category : Mathematics Languages : en Pages : 328
Book Description
Preface to the English Edition The present monograph is a revised and enlarged alternative of the author's monograph [19] which was devoted to the development of a unified approach to studying differential inclusions, whose values of the right hand sides are compact, not necessarily convex subsets of a Banach space. This approach relies on ideas and methods of modem functional analysis, general topology, the theory of multi-valued mappings and continuous selectors. Although the basic content of the previous monograph has been remained the same this monograph has been partly re-organized and the author's recent results have been added. The contents of the present book are divided into five Chapters and an Appendix. The first Chapter of the J>ook has been left without changes and deals with multi-valued differential equations generated by a differential inclusion. The second Chapter has been significantly revised and extended. Here the au thor's recent results concerning extreme continuous selectors of multi-functions with decomposable values, multi-valued selectors ofmulti-functions generated by a differential inclusion, the existence of solutions of a differential inclusion, whose right hand side has different properties of semicontinuity at different points, have been included. Some of these results made it possible to simplify schemes for proofs concerning the existence of solutions of differential inclu sions with semicontinuous right hand side a.nd to obtain new results. In this Chapter the existence of solutions of different types are considered.
Author: H.O. Fattorini Publisher: Elsevier ISBN: 0080872190 Category : Mathematics Languages : en Pages : 329
Book Description
Second order linear differential equations in Banach spaces can be used for modelling such second order equations of mathematical physics as the wave equation, the Klein-Gordon equation, et al. In this way, a unified treatment can be given to subjects such as growth of solutions, singular perturbation of parabolic, hyperbolic and Schrödinger type initial value problems, and the like. The book covers in detail these subjects as well as the applications to each specific problem.