Robustness of dynamically gradient multivalued dynamical systems

In this paper we study the robustness of dynamically gradient multivalued semiflows. As an application, we describe the dynamical properties of a family of Chafee-Infante problems approximating a differential inclusion studied in J. M. Arrieta, A. Rodríguez-Bernal and J. Valero, Dynamics of a reacti...

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Bibliographic Details
Authors: Caballero Toro, Rubén, Carvalho, Alexandre Nolasco, Marín Rubio, Pedro, Valero Cuadra, José
Format: article
Status:Versión enviada para evaluación y publicación
Publication Date:2019
Country:España
Institution:Universidad de Sevilla (US)
Repository:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/84141
Online Access:https://hdl.handle.net/11441/84141
https://doi.org/10.3934/dcdsb.2019006
Access Level:Open access
Keyword:Attractors
Reaction-diffusion equations
Stability
Dynamically gradient multivalued semiflows
Morse decomposition
Set-valued dynamical systems
Description
Summary:In this paper we study the robustness of dynamically gradient multivalued semiflows. As an application, we describe the dynamical properties of a family of Chafee-Infante problems approximating a differential inclusion studied in J. M. Arrieta, A. Rodríguez-Bernal and J. Valero, Dynamics of a reaction-diffusion equation with a discontinuous nonlinearity, International Journal of Bifurcation and Chaos, 16 (2006), 2965-2984, proving that the weak solutions of these problems generate a dynamically gradient multivalued semiflow with respect to suitable Morse sets.