Gradient inequalities with applications to asymptotic behavior and stability of gradient-like systems / Sen-Zhong Huang.

Format:

Book

Author/Creator:

Huang, Sen-Zhong, 1962- author.

Series:

Mathematical surveys and monographs ; v. 126.

Mathematical surveys and monographs, 0076-5376 ; volume 126

Language:

English

Subjects (All):

Topological dynamics.

Differential equations--Asymptotic theory.

Differential equations.

Variational inequalities (Mathematics).

Calculus of variations.

Physical Description:

1 online resource (194 p.)

Place of Publication:

Providence, Rhode Island : American Mathematical Society, [2006]

Language Note:

English

Summary:

This book presents a survey of the relatively new research field of gradient inequalities and their applications. The exposition emphasizes the powerful applications of gradient inequalities in studying asymptotic behavior and stability of gradient-like dynamical systems. It explains in-depth how gradient inequalities are established and how they can be used to prove convergence and stability of solutions to gradient-like systems. This book will serve as an introduction for furtherstudies of gradient inequalities and their applications in other fields, such as geometry and computer sciences. This book is written for advanced graduate students, researchers and applied mathematicians interested in dynamical systems and mathematical modeling.

Contents:

""Contents""; ""Preface""; ""Chapter 1 Introduction and overview of the results""; ""1. The methodology""; ""2. Convergence results for gradient-like trajectories""; ""3. Applications to gradient-like systems in Hilbert spaces""; ""4. Application to the stability problem""; ""5. Additional remarks""; ""Chapter 2 Gradient inequality""; ""1. Basic properties of gradient maps""; ""2. Gradient inequality""; ""3. Finite-dimensional gradient inequality""; ""4. Infinite-dimensional gradient inequality""; ""5. Variational gradient inequality""; ""6. Gradient inequality for monotone gradient maps""

""7. Optimal gradient inequality in Hilbert spaces""""8. Remarks on gradient inequalities of type G[sub(k)]""; ""Chapter 3 Abstract convergence results""; ""1. Gradient-like systems""; ""2. Three technical lemmas""; ""3. Convergence in gradient-like systems""; ""4. Convergence in Hilbert spaces""; ""5. Convergence in variational problems""; ""Chapter 4 Applications to semilinear gradient-like systems in Hilbert spaces""; ""1. The generic case""; ""2. The perfect case""; ""3. Results around the Laplacian operators""; ""4. Ginzburg-Landau models for superconductivity""

""5. Convergence in porous medium models""""Chapter 5 Applications to the stability problem""; ""1. Stability of ground states""; ""2. Convergence and stability of the steepest descent method""; ""3. The structure of equilibria sets of convergent systems""; ""4. Numeric test""; ""Bibliography""; ""Index""

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

Description based on print version record.

ISBN:

1-4704-1353-1