1 edition of **Evolution Equations in Scales of Banach Spaces** found in the catalog.

- 253 Want to read
- 1 Currently reading

Published
**2002**
by Vieweg+Teubner Verlag in Wiesbaden
.

Written in English

- Mathematics,
- Global analysis (Mathematics)

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.

**Edition Notes**

Statement | by Oliver Caps |

Series | Teubner-Texte zur Mathematik, 0138-502X -- 140, Teubner-Texte zur Mathematik -- 140. |

Classifications | |
---|---|

LC Classifications | QA299.6-433 |

The Physical Object | |

Format | [electronic resource] / |

Pagination | 1 online resource (309 pages). |

Number of Pages | 309 |

ID Numbers | |

Open Library | OL27037573M |

ISBN 10 | 3322800393 |

ISBN 10 | 9783322800398 |

OCLC/WorldCa | 840291387 |

itative properties of bounded solutions for some classes of abstract evolution equations in Banach spaces. In the last years, the theory of (maximal) regularity for linear evolution equations in abstract spaces, has been applied to the study of solutions . invertibility of the evolution operators on the whole space X (unlike the case of evolution operators generated by diﬀerential equations). 2. Exponential dichotomies of evolution operators Let X be a real or complex Banach space, B(X) be the Banach algebra of all bounded linear operators on X and J be a real interval which is R+ or R. The.

We study a problem of a parameter identification related to a linear evolution equation in a Banach space, using an additional information about the solution. For sufficiently regular data we provide an exact solution given by a Volterra integral equation, while for less regular data we obtain an approximating solution by an optimal control : Viorel Barbu, Gabriela Marinoschi. § 1. Metric properties of normed spaces 11 Duality mappings 11 Strictly convex normed spaces 13 Uniformly convex Banach spaces 14 § 2. Vectorial functions defined on real intervals 15 Absolutely continuous vectorial functions 15 Vectorial distributions and Wk'p spaces 18 Sobolev spaces 21 § 3.

Hyperbolic Equations, () Alberto Arosio HYPERBOLIC EQUATIONS IN BANACH SCALES INTRODUCTION A Banach scale is a familyf) (X of Banach spaces, indexed by a conti-nuous parameter r E ] O, R [ (R suc) h that X CX witI I X0f is denoted by0+ X. A Schauder basis in a Banach space X is a sequence {e n} n ≥ 0 of vectors in X with the property that for every vector x in X, there exist uniquely defined scalars {x n} n ≥ 0 depending on x, such that = ∑ = ∞, = (), ():= ∑. Banach spaces with a Schauder basis are necessarily separable, because the countable set of finite linear combinations with rational coefficients (say) is dense.

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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.

COVID Resources. Reliable information about the coronavirus (COVID) is available from the World Health Organization (current situation, international travel).Numerous and frequently-updated resource results are available from this ’s WebJunction has pulled together information and resources to assist library staff as they consider how to handle.

Get this from a library. Evolution Equations in Scales of Banach Spaces. [Oliver Caps] -- 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. The presen t volume contains the book-length text of a paper entitled "Nonlinear operators and nonlinear equations of evolution in Banach spaces" composed in its entiret y during the calendar year to be publishe d as par t of the Proceedings of the Symposium on Nonlinear Functional Analysis held in connection with the.

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 Author: Oliver Caps.

Abstract. So far we have studied linear parabolic evolution equations in a fixed Banach space. However, we have already seen, in connection with considerations of higher regularity and problems with variable Evolution Equations in Scales of Banach Spaces book, that it is useful and necessary to consider induced equations in interpolation spaces as : Herbert Amann.

A friendly introduction into geometry of Banach spaces. An Introduction to Banach Space Theory Graduate Texts in Mathematics. Robert E. Megginson. A more academic, but still very basic exposition. Topics in Banach space theory. Albiac, N. Kalton.

Though this is still a textbook, it contains a lot. Mostly for future Banach space specialists. The crucial ingredient consists of a suitable choice of multi-parameter scales of Banach function spaces and detailed analysis of integral equations in such spaces. com/locate/bulsci Global in time solutions of evolution equations in scales of Banach function spaces in R n Daniel Gourdin a,âˆ—, Todor Gramchev b a DÃ©partement de Cited by: Evolution Equations in Scales of Banach Spaces.

点击放大图片 出版社: Vieweg+teubner Verlag. 作者: Caps, Oliver 出版时间: 年07月15 日. 10位国际标准书号: 13位国际标准 Evolution Equations in Scales of Banach Spaces 英文书摘要.

Written by a distinguished specialist in functional analysis, this book presents a comprehensive treatment of the history of Banach spaces and (abstract bounded) linear operators.

While other historical texts on the subject focus on developments beforethis one is mainly devoted to the second half of the 20 th by: [Show full abstract] by using the general theory of quasi-linear evolution equations in nonreflexive Banach spaces, while the global existence of solution is obtained by the estimates of the Author: Alberto Arosio.

equations. 55 Strict L p solutions of fractional order equations. 61 5 Maximal regularit y in Hilb ert spaces via accretivit 71 Tw o classical results. 71 The case of nonlinear m-accretiv e op erators with 2 (0; 1). 72 iiiCited by: Nonlinear operators and nonlinear equations of evolution in Banach spaces (Proceedings of symposia in pure mathematics) by Felix E Browder (Author) › Visit Amazon's Felix E Browder Page.

Find all the books, read about the author, and more. See search results for this author. Are you an author.

Cited by: JOURNAL OF FUNCTIONAL ANALY () Semilinear Evolution Equations in Banach Spaces FRED B. WEISSLER* Department of Mathematics, The University of Texas, Austin, Texas Communicated by the Editors Received J ; revised Febru We study the evolution equation u'(t) = Au(t) + J(u(t)), t > 0, where e** is a Co semi Cited by: In this article we study the following nonlinear evolution equation.

x t t + A ∘ F x = g x, A − 1 2 x t, t ∈ 0, T, 0 Author: Kamal N. Soltanov. In this article, we are concerned with the existence of mild solutions as well as approximate controllability for a class of fractional evolution equations with. 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 Pages: Semilinear Evolution Equations in Banach Spaces FRED B. WEISSLER* Department of Mathematics, The Univem’ty of Texas, Austin, Texas Communicated by the Editors Received J ; revised Febru We study the evolution equation u’(t) = Au(t) + [email protected](t)), t > 0, where et” is a.

It includes related recent theorems in the field of harmonic analysis in Banach spaces and on operators possessing bounded imaginary powers. Lastly, there is a complete presentation of the technique of interpolation-extrapolation spaces and of evolution equations in those spaces, containing many new results.

homogeneous evolution equations in Banach spaces. The presented results can be utilized in future for an expansion of homogeneous feedback control design methods to evolution equations. The paper is organized as follows. The next section presents notations to be used in the paper.

Model description and basic assumptions are given in the section. () Positive solutions of operator equations on ordered Banach spaces and applications.

Computers & Mathematics with Applications() Exactly two positive solutions of nonhomogeneous semilinear elliptic equations in the by: The book also extends classical techniques, such as fixed points and stability methods, to abstract functional differential equations with applications to partial functional differential equations.

Almost Periodic Solutions of Differential Equations in Banach Spaces will appeal to anyone working in mathematical analysis.This book can be studied in a variety of ways and for di erent motivations. The principal, but not the only, audience that we have in mind consists of researchers who need and use Analysis in Banach Spaces as a tool for studying other problems, in particular the regularity of evolution equations mentioned above.