Attractors for gradient flows of non convex functionals and applications

2007/05/31 by Riccarda Rossi, Rossi, Riccarda, Antonio Segatti +3
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Mathematical Biology Tumor Growth #Stability and Controllability of Differential Equations #math.AP #msc:35K55 #msc:37L30 #msc:80A22

paper · pdf · doi:10.48550/arxiv.0705.4531

46 pages

arxiv created 2007/05/31 · arxiv updated 2009/12/01

Abstract

This paper addresses the long-time behavior of gradient flows of non convex functionals in Hilbert spaces. Exploiting the notion of generalized semiflows by J. M. Ball, we provide some sufficient conditions for the existence of a global attractor. The abstract results are applied to various classes of non convex evolution problems. In particular, we discuss the long-time behavior of solutions of quasi-stationary phase field models and prove the existence of a global attractor.

Related

• Global attractors for gradient flows in metric spaces
• Global attractors for doubly nonlinear evolution equations with non-monotone perturbations
• Global attractors for multivalued semiflows with weak continuity properties
• A gradient flow generated by a nonlocal model of a neural field in an unbounded domain
• Dissipative property for a class of non local evolution equations