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Abstract Parabolic Evolution Equations and ?ojasiewicz-Simon Inequality I: Abstract Theory (SpringerBriefs in Mathematics)
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Abstract Parabolic Evolution Equations and ?ojasiewicz-Simon Inequality II: Applications (SpringerBriefs in Mathematics)
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Abstract Parabolic Evolution Equations A
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Abstract Parabolic Evolution Equations A
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Abstract Parabolic Evolution Equations and Lojasiewicz-Simon Inequality I
Language: English
Published by Springer Nature Singapore, 2021
ISBN 10: 981161895X ISBN 13: 9789811618956
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Condition: Sehr gut. Zustand: Sehr gut | Sprache: Englisch | Produktart: Bücher | The classical Lojasiewicz gradient inequality (1963) was extended by Simon (1983) to the infinite-dimensional setting, now called the Lojasiewicz-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 Lojasiewicz-Simon gradient inequality.In order to apply the abstract results to a wider class of concrete nonlinear parabolic equations, the usual Lojasiewicz-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.
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Abstract Parabolic Evolution Equations and żojasiewicz-Simon Inequality II
Language: English
Published by Springer Nature Singapore, Springer Nature Singapore Aug 2021, 2021
ISBN 10: 9811626626 ISBN 13: 9789811626623
Seller: buchversandmimpf2000, Emtmannsberg, BAYE, Germany
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Taschenbuch. Condition: Neu. Neuware -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 żojasiewiczżSimon 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.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 140 pp. Englisch.
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Taschenbuch. Condition: Neu. Abstract Parabolic Evolution Equations and żojasiewicz-Simon Inequality II | Applications | Atsushi Yagi | Taschenbuch | SpringerBriefs in Mathematics | ix | Englisch | 2021 | Springer | EAN 9789811626623 | Verantwortliche Person für die EU: Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg, juergen[dot]hartmann[at]springer[dot]com | Anbieter: preigu.
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Taschenbuch. Condition: Neu. Druck auf Anfrage Neuware - Printed after ordering - 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 Lojasiewicz-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-dimensionalspaces. 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.
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Taschenbuch. Condition: Neu. Abstract Parabolic Evolution Equations and Lojasiewicz-Simon Inequality I | Abstract Theory | Atsushi Yagi | Taschenbuch | x | Englisch | 2021 | Springer Singapore | EAN 9789811618956 | Verantwortliche Person für die EU: Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg, juergen[dot]hartmann[at]springer[dot]com | Anbieter: preigu.
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Abstract Parabolic Evolution Equations and their Applications (Springer Monographs in Mathematics)
Book 67 of 187: Springer Monographs in MathematicsSeller: Ria Christie Collections, Uxbridge, United Kingdom
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Abstract Parabolic Evolution Equations and żojasiewicz-Simon Inequality I : Abstract Theory
Language: English
Published by Springer Nature B.V., 2021
ISBN 10: 981161895X ISBN 13: 9789811618956
Taschenbuch. Condition: Neu. Druck auf Anfrage Neuware - Printed after ordering - The classical Lojasiewicz gradient inequality (1963) was extended by Simon (1983) to the infinite-dimensional setting, now called the Lojasiewicz-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 Lojasiewicz-Simon gradient inequality.In order to apply the abstract results to a wider class of concrete nonlinear parabolic equations, the usual Lojasiewicz-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.
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Abstract Parabolic Evolution Equations and their Applications (Springer Monographs in Mathematics)
Book 67 of 187: Springer Monographs in MathematicsSeller: Ria Christie Collections, Uxbridge, United Kingdom
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Abstract Parabolic Evolution Equations and Their Applications
Book 67 of 187: Springer Monographs in MathematicsSeller: GreatBookPricesUK, Woodford Green, United Kingdom
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Abstract Parabolic Evolution Equations and Their Applications
Book 67 of 187: Springer Monographs in MathematicsSeller: GreatBookPricesUK, Woodford Green, United Kingdom
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Abstract Parabolic Evolution Equations and their Applications
Book 67 of 187: Springer Monographs in MathematicsLanguage: English
Published by Springer Berlin Heidelberg, 2012
ISBN 10: 3642261795 ISBN 13: 9783642261794
Taschenbuch. Condition: Neu. Druck auf Anfrage Neuware - Printed after ordering - 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.
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