Abstract Parabolic Evolution Equations And Ojasiewicz Simon Inequality Ii
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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 I
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Author : Atsushi Yagi
language : en
Publisher: Springer Nature
Release Date : 2021-05-31
Abstract Parabolic Evolution Equations And Ojasiewicz Simon Inequality I 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 2021-05-31 with Mathematics categories.
The classical Łojasiewicz gradient inequality (1963) was extended by Simon (1983) to the infinite-dimensional setting, now called the Łojasiewicz–Simon gradient inequality. This book presents a unified method to show asymptotic convergence of solutions to a stationary solution for abstract parabolic evolution equations of the gradient form by utilizing this Łojasiewicz–Simon gradient inequality. In order to apply the abstract results to a wider class of concrete nonlinear parabolic equations, the usual Łojasiewicz–Simon inequality is extended, which is published here for the first time. In the second version, these abstract results are applied to reaction–diffusion equations with discontinuous coefficients, reaction–diffusion systems, and epitaxial growth equations. The results are also applied to the famous chemotaxis model, i.e., the Keller–Segel equations even for higher-dimensional ones.
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 Parabolic Evolution Equations And Ojasiewicz Simon Inequality I
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Author : Atsushi Yagi
language : en
Publisher:
Release Date : 2021
Abstract Parabolic Evolution Equations And Ojasiewicz Simon Inequality I 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 Differential equations, Parabolic categories.
The classical ojasiewicz gradient inequality (1963) was extended by Simon (1983) to the infinite-dimensional setting, now called the ojasiewiczSimon gradient inequality. This book presents a unified method to show asymptotic convergence of solutions to a stationary solution for abstract parabolic evolution equations of the gradient form by utilizing this ojasiewiczSimon gradient inequality. In order to apply the abstract results to a wider class of concrete nonlinear parabolic equations, the usual ojasiewiczSimon inequality is extended, which is published here for the first time. In the second version, these abstract results are applied to reactiondiffusion equations with discontinuous coefficients, reactiondiffusion systems, and epitaxial growth equations. The results are also applied to the famous chemotaxis model, i.e., the KellerSegel equations even for higher-dimensional ones.
Abstract Evolution Equations Periodic Problems And Applications
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Author : D Daners
language : en
Publisher: Chapman and Hall/CRC
Release Date : 1992-12-29
Abstract Evolution Equations Periodic Problems And Applications written by D Daners and has been published by Chapman and Hall/CRC this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-12-29 with Mathematics categories.
Part of the Pitman Research Notes in Mathematics series, this text covers: linear evolution equations of parabolic type; semilinear evolution equations of parabolic type; evolution equations and positivity; semilinear periodic evolution equations; and applications.
Evolution Equations
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Author : Kaïs Ammari
language : en
Publisher: Cambridge University Press
Release Date : 2018
Evolution Equations written by Kaïs Ammari and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018 with Mathematics categories.
The proceedings of a summer school held in 2015 whose theme was long time behavior and control of evolution equations.
Evolution Equations
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Author : Gisele Ruiz Goldstein
language : en
Publisher: CRC Press
Release Date : 2019-04-24
Evolution Equations written by Gisele Ruiz Goldstein and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-04-24 with Mathematics categories.
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 li
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.
Semigroup Theory And Evolution Equations
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Author : Philippe Clement
language : en
Publisher: CRC Press
Release Date : 2023-05-31
Semigroup Theory And Evolution Equations written by Philippe Clement and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-05-31 with Mathematics categories.
Proceedings of the Second International Conference on Trends in Semigroup Theory and Evolution Equations held Sept. 1989, Delft University of Technology, the Netherlands. Papers deal with recent developments in semigroup theory (e.g., positive, dual, integrated), and nonlinear evolution equations (e
Abstract Evolution Equations Periodic Problems And Applications
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Author : Daniel Daners
language : en
Publisher: Longman Sc & Tech
Release Date : 1992
Abstract Evolution Equations Periodic Problems And Applications written by Daniel Daners and has been published by Longman Sc & Tech this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Mathematics categories.