APPLICATIONS OF THE ŁOJASIEWICZ–SIMON, GRADIENT INEQUALITY TO GRADIENT-LIKE EVOLUTION EQUATIONS-Reference-Cited by-同舟云学术

APPLICATIONS OF THE ŁOJASIEWICZ–SIMON, GRADIENT INEQUALITY TO GRADIENT-LIKE EVOLUTION EQUATIONS

Published:2009-10 Issue:04 Volume:07 Page:351-372
ISSN:0219-5305
Container-title:Analysis and Applications
language:en
Short-container-title:Anal. Appl.

Author:

CHILL RALPH¹,HARAUX ALAIN²,JENDOUBI MOHAMED ALI³

Affiliation:

1. Université Paul Verlaine-Metz et CNRS, Laboratoire de Mathématiques et Applications de Metz, UMR 7122, Bât. A, Ile du Saulcy, 57045 Metz Cedex 1, France

2. Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie et CNRS, Boîte courrier 187, 75252 Paris Cedex 05, France

3. Faculté des sciences de Bizerte, Département de Mathématiques, 7021 Jarzouna Bizerte, Tunisia

Abstract

We prove convergence to equilibrium of global and bounded solutions of gradient-like evolution equations. Our abstract results are illustrated by several examples in finite and infinite dimensions.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Analysis

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0219530509001438

Reference33 articles.

1. A second-order gradient-like dissipative dynamical system with Hessian-driven damping.

2. THE HEAVY BALL WITH FRICTION METHOD, I. THE CONTINUOUS DYNAMICAL SYSTEM: GLOBAL EXPLORATION OF THE LOCAL MINIMA OF A REAL-VALUED FUNCTION BY ASYMPTOTIC ANALYSIS OF A DISSIPATIVE DYNAMICAL SYSTEM

3. On the asymptotic behavior of generalized processes, with applications to nonlinear evolution equations

4. Stability Theory of Dynamical Systems

5. CONVERGENCE TO EQUILIBRIUM FOR SEMILINEAR PARABOLIC PROBLEMS IN

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