$\mathcal {R}$-Boundedness, Fourier Multipliers and Problems of Elliptic and Parabolic Type PDF Download

Author: Robert Denk
Publisher: American Mathematical Soc.
ISBN: 0821833782
Category : Mathematics
Languages : en
Pages : 130

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Book Description
The property of maximal $L_p$-regularity for parabolic evolution equations is investigated via the concept of $\mathcal R$-sectorial operators and operator-valued Fourier multipliers. As application, we consider the $L_q$-realization of an elliptic boundary value problem of order $2m$ with operator-valued coefficients subject to general boundary conditions. We show that there is maximal $L_p$-$L_q$-regularity for the solution of the associated Cauchy problem provided the top order coefficients are bounded and uniformly continuous.

Author: Robert Denk
Publisher: American Mathematical Society(RI)
ISBN: 9781470403867
Category : Boundary value problems
Languages : en
Pages : 114

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Book Description
Introduction Notations and conventions $\mathcal R$-Boundedness and Sectorial Operators: Sectorial operators The classes ${\mathcal{BIP}}(X)$ and $\mathcal H^\infty(X)$ $\mathcal R$-bounded families of operators $\mathcal R$-sectorial operators and maximal $L_p$-regularity Elliptic and Parabolic Boundary Value Problems: Elliptic differential operators in $L_p(\mathbb{R}^n;E)$ Elliptic problems in a half space: General Banach spaces Elliptic problems in a half space: Banach spaces of class $\mathcal{HT}$ Elliptic and parabolic problems in domains Notes References.

Author: Robert Denk
Publisher:
ISBN: 9780821833780
Category : Boundary value problems
Languages : en
Pages : 114

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Book Description

Author: Angelo Favini
Publisher: Springer
ISBN: 3319114069
Category : Mathematics
Languages : en
Pages : 472

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Book Description
This book, based on a selection of talks given at a dedicated meeting in Cortona, Italy, in June 2013, shows the high degree of interaction between a number of fields related to applied sciences. Applied sciences consider situations in which the evolution of a given system over time is observed, and the related models can be formulated in terms of evolution equations (EEs). These equations have been studied intensively in theoretical research and are the source of an enormous number of applications. In this volume, particular attention is given to direct, inverse and control problems for EEs. The book provides an updated overview of the field, revealing its richness and vitality.

Author: Atsushi Yagi
Publisher: Springer Science & Business Media
ISBN: 3642046312
Category : Mathematics
Languages : en
Pages : 594

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Book Description
This monograph is intended to present the fundamentals of the theory of abstract parabolic evolution equations and to show how to apply to various nonlinear dif- sion equations and systems arising in science. The theory gives us a uni?ed and s- tematic treatment for concrete nonlinear diffusion models. Three main approaches are known to the abstract parabolic evolution equations, namely, the semigroup methods, the variational methods, and the methods of using operational equations. In order to keep the volume of the monograph in reasonable length, we will focus on the semigroup methods. For other two approaches, see the related references in Bibliography. The semigroup methods, which go back to the invention of the analytic se- groups in the middle of the last century, are characterized by precise formulas representing the solutions of the Cauchy problem for evolution equations. The ?tA analytic semigroup e generated by a linear operator ?A provides directly a fundamental solution to the Cauchy problem for an autonomous linear e- dU lution equation, +AU =F(t), 0

Author: Luigi G. Rodino
Publisher: Springer
ISBN: 3030008746
Category : Mathematics
Languages : en
Pages : 207

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Book Description
This book includes the texts of the survey lectures given by plenary speakers at the 11th International ISAAC Congress held in Växjö, Sweden, on 14-18 August, 2017. It is the purpose of ISAAC to promote analysis, its applications, and its interaction with computation. Analysis is understood here in the broad sense of the word, including differential equations, integral equations, functional analysis, and function theory. With this objective, ISAAC organizes international Congresses for the presentation and discussion of research on analysis. The plenary lectures in the present volume, authored by eminent specialists, are devoted to some exciting recent developments, topics including: local solvability for subprincipal type operators; fractional-order Laplacians; degenerate complex vector fields in the plane; lower bounds for pseudo-differential operators; a survey on Morrey spaces; localization operators in Signal Theory and Quantum Mechanics. Thanks to the accessible style used, readers only need a basic command of Calculus. This book will appeal to scientists, teachers, and graduate students in Mathematics, in particular Mathematical Analysis, Probability and Statistics, Numerical Analysis and Mathematical Physics.

Author: Wolfgang Arendt
Publisher: Birkhäuser
ISBN: 3034879245
Category : Mathematics
Languages : en
Pages : 803

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Book Description
Philippe Bénilan was a most original and charismatic mathematician who had a deep and decisive impact on the theory of Nonlinear Evolution Equations. Dedicated to him, Nonlinear Evolution Equations and Related Topics contains research papers written by highly distinguished mathematicians. They are all related to Philippe Benilan's work and reflect the present state of this most active field. The contributions cover a wide range of nonlinear and linear equations.

Author: Tomáš Bodnár
Publisher: Springer Nature
ISBN: 3031276256
Category : Mathematics
Languages : en
Pages : 364

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Book Description
This volume presents state-of-the-art developments in theoretical and applied fluid mechanics. Chapters are based on lectures given at a workshop in the summer school Fluids under Control, held in Prague on August 25, 2021. Readers will find a thorough analysis of current research topics, presented by leading experts in their respective fields. Specific topics covered include: Magnetohydrodynamic systems The steady Navier-Stokes-Fourier system Boussinesq equations Fluid-structure-acoustic interactions Fluids under Control will be a valuable resource for students interested in mathematical fluid mechanics.

Author: Tohru Ozawa
Publisher: Springer Nature
ISBN: 3031192524
Category : Mathematics
Languages : en
Pages : 396

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Book Description
Yoshihiro Shibata has made many significant contributions to the area of mathematical fluid mechanics over the course of his illustrious career, including landmark work on the Navier-Stokes equations. The papers collected here — on the occasion of his 70th birthday — are written by world-renowned researchers and celebrate his decades of outstanding achievements.

Author: Chiun Chuan Chen
Publisher: World Scientific
ISBN: 9814480843
Category : Mathematics
Languages : en
Pages : 285

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Book Description
The book is an account on recent advances in elliptic and parabolic problems and related equations, including general quasi-linear equations, variational structures, Bose-Einstein condensate, Chern-Simons model, geometric shell theory and stability in fluids. It presents very up-to-date research on central issues of these problems such as maximal regularity, bubbling, blowing-up, bifurcation of solutions and wave interaction. The contributors are well known leading mathematicians and prominent young researchers.The proceedings have been selected for coverage in:• Index to Scientific & Technical Proceedings® (ISTP® / ISI Proceedings)• Index to Scientific & Technical Proceedings (ISTP CDROM version / ISI Proceedings)• CC Proceedings — Engineering & Physical Sciences