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Author: Viorel Barbu
Publisher: Springer Science & Business Media
ISBN: 1441955429
Category : Mathematics
Languages : en
Pages : 283
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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: Viorel Barbu
Publisher: Springer Science & Business Media
ISBN: 1441955429
Category : Mathematics
Languages : en
Pages : 283
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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: R. E. Showalter
Publisher: American Mathematical Soc.
ISBN: 0821893971
Category : Mathematics
Languages : en
Pages : 296
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Book Description
The objectives of this monograph are to present some topics from the theory of monotone operators and nonlinear semigroup theory which are directly applicable to the existence and uniqueness theory of initial-boundary-value problems for partial differential equations and to construct such operators as realizations of those problems in appropriate function spaces. A highlight of this presentation is the large number and variety of examples introduced to illustrate the connection between the theory of nonlinear operators and partial differential equations. These include primarily semilinear or quasilinear equations of elliptic or of parabolic type, degenerate cases with change of type, related systems and variational inequalities, and spatial boundary conditions of the usual Dirichlet, Neumann, Robin or dynamic type. The discussions of evolution equations include the usual initial-value problems as well as periodic or more general nonlocal constraints, history-value problems, those which may change type due to a possibly vanishing coefficient of the time derivative, and other implicit evolution equations or systems including hysteresis models. The scalar conservation law and semilinear wave equations are briefly mentioned, and hyperbolic systems arising from vibrations of elastic-plastic rods are developed. The origins of a representative sample of such problems are given in the appendix.
Author: Felix E. Browder
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 328
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Book Description
Author: Felix E. Browder
Publisher:
ISBN:
Category : Banach spaces
Languages : en
Pages : 308
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Book Description
Author: Charles Chidume
Publisher: Springer Science & Business Media
ISBN: 1848821891
Category : Mathematics
Languages : en
Pages : 337
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Book Description
The contents of this monograph fall within the general area of nonlinear functional analysis and applications. We focus on an important topic within this area: geometric properties of Banach spaces and nonlinear iterations, a topic of intensive research e?orts, especially within the past 30 years, or so. In this theory, some geometric properties of Banach spaces play a crucial role. In the ?rst part of the monograph, we expose these geometric properties most of which are well known. As is well known, among all in?nite dim- sional Banach spaces, Hilbert spaces have the nicest geometric properties. The availability of the inner product, the fact that the proximity map or nearest point map of a real Hilbert space H onto a closed convex subset K of H is Lipschitzian with constant 1, and the following two identities 2 2 2 ||x+y|| =||x|| +2 x,y +||y|| , (?) 2 2 2 2 ||?x+(1??)y|| = ?||x|| +(1??)||y|| ??(1??)||x?y|| , (??) which hold for all x,y? H, are some of the geometric properties that char- terize inner product spaces and also make certain problems posed in Hilbert spaces more manageable than those in general Banach spaces. However, as has been rightly observed by M. Hazewinkel, “... many, and probably most, mathematical objects and models do not naturally live in Hilbert spaces”. Consequently,toextendsomeoftheHilbertspacetechniquestomoregeneral Banach spaces, analogues of the identities (?) and (??) have to be developed.
Author: Isao Miyadera
Publisher: American Mathematical Soc.
ISBN: 9780821886816
Category : Mathematics
Languages : en
Pages : 246
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Book Description
This book presents a systematic exposition of the general theory of nonlinear contraction semigroups in Banach spaces and is aimed at students and researchers in science and engineering as well as in mathematics. Suitable for use as a textbook in graduate courses and seminars, this self-contained book is accessible to those with only a basic knowledge of functional analysis. After preprequisites presented in the first chapter, Miyadera covers the basic properties of dissipative operators and nonlinear contraction semigroups in Banach spaces. The generation of nonlinear contraction semigroups, the Komura theorem, and the Crandall-Liggett theorem are explored, and there is a treatment of the convergence of difference approximation of Cauchy problems for ????- dissipative operators and the Kobayashi generation theorem of nonlinear semigroups. Nonlinear Semigroups concludes with applications to nonlinear evolution equations and to first order quasilinear equations.
Author: Kazufumi Ito
Publisher: World Scientific
ISBN: 9789812380265
Category : Science
Languages : en
Pages : 524
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Book Description
Annotation Ito (North Carolina State U.) and Kappel (U. of Graz, Austria) offer a unified presentation of the general approach for well-posedness results using abstract evolution equations, drawing from and modifying the work of K. and Y. Kobayashi and S. Oharu. They also explore abstract approximation results for evolution equations. Their work is not a textbook, but they explain how instructors can use various sections, or combinations of them, as a foundation for a range of courses. Annotation copyrighted by Book News, Inc., Portland, OR
Author: Simeon Reich
Publisher: Imperial College Press
ISBN: 1860945759
Category : Mathematics
Languages : en
Pages : 374
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Book Description
Nonlinear semigroup theory is not only of intrinsic interest, but is also important in the study of evolution problems. In the last forty years, the generation theory of flows of holomorphic mappings has been of great interest in the theory of Markov stochastic branching processes, the theory of composition operators, control theory, and optimization. It transpires that the asymptotic behavior of solutions to evolution equations is applicable to the study of the geometry of certain domains in complex spaces.Readers are provided with a systematic overview of many results concerning both nonlinear semigroups in metric and Banach spaces and the fixed point theory of mappings, which are nonexpansive with respect to hyperbolic metrics (in particular, holomorphic self-mappings of domains in Banach spaces). The exposition is organized in a readable and intuitive manner, presenting basic functional and complex analysis as well as very recent developments.
Author: Michael G. Crandall
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 282
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Book Description
This volume constitutes the proceedings of the Symposium on Nonlinear Evolution Equations held in Madison, October 17-19, 1977. The thirteen papers presented herein follow the order of the corresponding lectures. This symposium was sponsored by the Army Research Office, the National Science Foundation, and the Office of Naval Research.
Author: Felix E. Browder
Publisher: American Mathematical Soc.
ISBN: 0821814710
Category : Mathematics
Languages : en
Pages : 556
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Book Description
