Functional Analytic Methods For Evolution Equations

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Functional Analytic Methods For Evolution Equations

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Author : Giuseppe Da Prato
language : en
Publisher: Springer Science & Business Media
Release Date : 2004-09-22

Functional Analytic Methods For Evolution Equations written by Giuseppe Da Prato and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-09-22 with Mathematics categories.

This book consists of five introductory contributions by leading mathematicians on the functional analytic treatment of evolutions equations. In particular the contributions deal with Markov semigroups, maximal L^p-regularity, optimal control problems for boundary and point control systems, parabolic moving boundary problems and parabolic nonautonomous evolution equations. The book is addressed to PhD students, young researchers and mathematicians doing research in one of the above topics.

Functional Analytic Methods For Evolution Equations

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Author :
language : en
Publisher:
Release Date : 2004

Functional Analytic Methods For Evolution Equations written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Evolution equations categories.

Functional Analytic Methods For Partial Differential Equations

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Author : Hiroki Tanabe
language : en
Publisher: CRC Press
Release Date : 2017-11-22

Functional Analytic Methods For Partial Differential Equations written by Hiroki Tanabe and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-22 with Mathematics categories.

Combining both classical and current methods of analysis, this text present discussions on the application of functional analytic methods in partial differential equations. It furnishes a simplified, self-contained proof of Agmon-Douglis-Niremberg's Lp-estimates for boundary value problems, using the theory of singular integrals and the Hilbert transform.

Functional Analytic Methods For Partial Differential Equations

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Author : Hiroshi Fujita
language : en
Publisher: Springer
Release Date : 2006-11-14

Functional Analytic Methods For Partial Differential Equations written by Hiroshi Fujita and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.

Proceedings of the International Conference on Functional Analysis and Its Application in Honor of Professor Tosio Kato, July 3-6, 1989, University of Tokyo, and the Symposium on Spectral and Scattering Theory, held July 7, 1989, at Gakushin University, Tokyo.

Abstract Parabolic Evolution Equations And Ojasiewicz Simon Inequality Ii

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Author : Atsushi Yagi
language : en
Publisher: Springer Nature
Release Date : 2021-08-12

Abstract Parabolic Evolution Equations And Ojasiewicz Simon Inequality Ii written by Atsushi Yagi and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-08-12 with Mathematics categories.

This second volume continues the study on asymptotic convergence of global solutions of parabolic equations to stationary solutions by utilizing the theory of abstract parabolic evolution equations and the Łojasiewicz–Simon gradient inequality. In the first volume of the same title, after setting the abstract frameworks of arguments, a general convergence theorem was proved under the four structural assumptions of critical condition, Lyapunov function, angle condition, and gradient inequality. In this volume, with those abstract results reviewed briefly, their applications to concrete parabolic equations are described. Chapter 3 presents a discussion of semilinear parabolic equations of second order in general n-dimensional spaces, and Chapter 4 is devoted to treating epitaxial growth equations of fourth order, which incorporate general roughening functions. In Chapter 5 consideration is given to the Keller–Segel equations in one-, two-, and three-dimensional spaces. Some of these results had already been obtained and published by the author in collaboration with his colleagues. However, by means of the abstract theory described in the first volume, those results can be extended much more. Readers of this monograph should have a standard-level knowledge of functional analysis and of function spaces. Familiarity with functional analytic methods for partial differential equations is also assumed.

Abstract Parabolic Evolution Equations And Ojasiewicz Simon Inequality Ii

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Author : Atsushi Yagi
language : en
Publisher:
Release Date : 2021

Abstract Parabolic Evolution Equations And Ojasiewicz Simon Inequality Ii written by Atsushi Yagi and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021 with categories.

This second volume continues the study on asymptotic convergence of global solutions of parabolic equations to stationary solutions by utilizing the theory of abstract parabolic evolution equations and the Łojasiewicz-Simon gradient inequality. In the first volume of the same title, after setting the abstract frameworks of arguments, a general convergence theorem was proved under the four structural assumptions of critical condition, Lyapunov function, angle condition, and gradient inequality. In this volume, with those abstract results reviewed briefly, their applications to concrete parabolic equations are described. Chapter 3 presents a discussion of semilinear parabolic equations of second order in general n-dimensional spaces, and Chapter 4 is devoted to treating epitaxial growth equations of fourth order, which incorporate general roughening functions. In Chapter 5 consideration is given to the Keller-Segel equations in one-, two-, and three-dimensional spaces. Some of these results had already been obtained and published by the author in collaboration with his colleagues. However, by means of the abstract theory described in the first volume, those results can be extended much more. Readers of this monograph should have a standard-level knowledge of functional analysis and of function spaces. Familiarity with functional analytic methods for partial differential equations is also assumed.

Abstract And Applied Analysis

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Author : N. M. Chuong
language : en
Publisher: World Scientific
Release Date : 2004

Abstract And Applied Analysis written by N. M. Chuong and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mathematics categories.

This volume takes up various topics in Mathematical Analysis including boundary and initial value problems for Partial Differential Equations and Functional Analytic methods. Topics include linear elliptic systems for composite material OCo the coefficients may jump from domain to domain; Stochastic Analysis OCo many applied problems involve evolution equations with random terms, leading to the use of stochastic analysis. The proceedings have been selected for coverage in: . OCo Index to Scientific & Technical Proceedings (ISTP CDROM version / ISI Proceedings). OCo CC Proceedings OCo Engineering & Physical Sciences. Contents: Deterministic Analysis: Differentiation of Hypergeometric Functions with Respect to Parameters (Yu A Brychkov & K O Geddes); On the Lagrange Problem About the Strongest Columns (Yu V Egorov); Wavelet Based Fast Solution of Boundary Integral Equations (H Harbrecht & R Schneider); Semi-Classical Methods in GinzburgOCoLandau Theory (B Helffer); Stability of Equilibriums in One-Dimensional Motion of Compressible Viscous Gas Forced by Self-Gravity (Y Iwata & Y Yamamoto); Estimates for Elliptic Systems for Composite Material (L Nirenberg); On Asymptotics for the Mabuchi Energy Functional (D H Phong & J Sturm); Regularity of Solutions of the Initial Boundary Value Problem for Linearized Equations of Ideal Magneto-Hydrodynamics (M Yamamoto); Stochastic Analysis: Impulsive Stochastic Evolution Inclusions with Multi-Valued Diffusion (N U Ahmed); Some of Future Directions of White Noise Analysis (T Hida); Constructing Random Probability Distributions (T P Hill & D E R Sitton); Multiparameter Additive Processes of Mixture Type (K Inoue); The Random Integral Representation Hypothesis Revisited: New Classes of S-Selfdecomposable Laws (Z J Jurek); Semigroups and Processes with Parameter in a Cone (J Pedersen & K-I Sato); and other papers. Readership: Researchers and academics in the fields of analysis and differential equations, approximation theory, probability and statistics."

Current Trends In Analysis And Its Applications

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Author : Vladimir V. Mityushev
language : en
Publisher: Birkhäuser
Release Date : 2015-02-04

Current Trends In Analysis And Its Applications written by Vladimir V. Mityushev and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-02-04 with Mathematics categories.

This book is a collection of papers from the 9th International ISAAC Congress held in 2013 in Kraków, Poland. The papers are devoted to recent results in mathematics, focused on analysis and a wide range of its applications. These include up-to-date findings of the following topics: - Differential Equations: Complex and Functional Analytic Methods - Nonlinear PDE - Qualitative Properties of Evolution Models - Differential and Difference Equations - Toeplitz Operators - Wavelet Theory - Topological and Geometrical Methods of Analysis - Queueing Theory and Performance Evaluation of Computer Networks - Clifford and Quaternion Analysis - Fixed Point Theory - M-Frame Constructions - Spaces of Differentiable Functions of Several Real Variables Generalized Functions - Analytic Methods in Complex Geometry - Topological and Geometrical Methods of Analysis - Integral Transforms and Reproducing Kernels - Didactical Approaches to Mathematical Thinking Their wide applications in biomathematics, mechanics, queueing models, scattering, geomechanics etc. are presented in a concise, but comprehensible way, such that further ramifications and future directions can be immediately seen.

Evolution Equations With A Complex Spatial Variable

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Author : Ciprian G Gal
language : en
Publisher: World Scientific
Release Date : 2014-03-18

Evolution Equations With A Complex Spatial Variable written by Ciprian G Gal and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-03-18 with Mathematics categories.

This book investigates several classes of partial differential equations of real time variable and complex spatial variables, including the heat, Laplace, wave, telegraph, Burgers, Black–Merton–Scholes, Schrödinger and Korteweg–de Vries equations. The complexification of the spatial variable is done by two different methods. The first method is that of complexifying the spatial variable in the corresponding semigroups of operators. In this case, the solutions are studied within the context of the theory of semigroups of linear operators. It is also interesting to observe that these solutions preserve some geometric properties of the boundary function, like the univalence, starlikeness, convexity and spirallikeness. The second method is that of complexifying the spatial variable directly in the corresponding evolution equation from the real case. More precisely, the real spatial variable is replaced by a complex spatial variable in the corresponding evolution equation and then analytic and non-analytic solutions are sought. For the first time in the book literature, we aim to give a comprehensive study of the most important evolution equations of real time variable and complex spatial variables. In some cases, potential physical interpretations are presented. The generality of the methods used allows the study of evolution equations of spatial variables in general domains of the complex plane. Contents:Historical Background and MotivationHeat and Laplace Equations of Complex Spatial VariablesHigher-Order Heat and Laplace Equations with Complex Spatial VariablesWave and Telegraph Equations with Complex Spatial VariablesBurgers and Black–Merton–Scholes Equations with Complex Spatial VariablesSchrödinger-Type Equations with Complex Spatial VariablesLinearized Korteweg–de Vries Equations with Complex Spatial VariablesEvolution Equations with a Complex Spatial Variable in General Domains Readership: Graduates and researchers in partial differential equations and in classical analytical function theory of one complex variable. Key Features:For the first time in literature, the study of evolution equations of real time variable and complex spatial variables is madeThe study includes some of the most important classes of partial differential equations: heat, Laplace, wave, telegraph, Burgers, Black–Merton–Scholes, Schrodinger and Korteweg–de Vries equationsThe book is entirely based on the authors' own workKeywords:Evolution Equations of Complex Spatial Variables;Semigroup of Linear Operators;Complex Convolution Integrals;Heat;Laplace;Wave;Telegraph;Burgers;Black–Merton–Scholes;Schrodinger;Korteweg–de Vries Equations

Evolution Equations In Scales Of Banach Spaces

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Author : Oliver Caps
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Evolution Equations In Scales Of Banach Spaces written by Oliver Caps and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

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.