# American Institute of Mathematical Sciences

March  2019, 24(3): 1049-1077. doi: 10.3934/dcdsb.2019006

## Robustness of dynamically gradient multivalued dynamical systems

 1 Centro de Investigación Operativa, Universidad Miguel Hernández de Elche, 03202-Elche, Alicante, Spain 2 Instituto de Ciências Matemáticas e de Computaçao, Universidade de São Paulo, Campus de São Carlos, Caixa Postal 668, 13560-970 São Carlos, SP, Brazil 3 Departamento de Ecuaciones Diferenciales y Análisis Numérico, Universidad de Sevilla, c/Tarfia s/n, 41012-Sevilla, Spain 4 Centro de Investigación Operativa, Universidad Miguel Hernández de Elche, 03202-Elche, Alicante, Spain

To Professor Valery Melnik, in Memoriam

Received  January 2018 Revised  May 2018 Published  January 2019

Fund Project: The authors of this work have been partially funded by the following projects: R. Caballero is a fellow of Programa de FPU del Ministerio de Educación, Cultura y Deporte, reference FPU15/03080; P. Marín-Rubio was supported by projects PHB2010-0002-PC (Ministerio de Educación-DGPU), MTM2015-63723-P (MINECO/FEDER, EU) and P12-FQM-1492 (Junta de Andalucía); A. N. Carvalho was supported by grant 2018/10997-6 from FAPESP-Brazil and grant 303929/2015-4 from CNPq-Brazil; and J.Valero by projects MTM2015-63723-P, MTM2016-74921-P (MINECO/FEDER, EU) and P12-FQM-1492 (Junta de Andalucía).

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 [3], proving that the weak solutions of these problems generate a dynamically gradient multivalued semiflow with respect to suitable Morse sets.

Citation: Rubén Caballero, Alexandre N. Carvalho, Pedro Marín-Rubio, José Valero. Robustness of dynamically gradient multivalued dynamical systems. Discrete & Continuous Dynamical Systems - B, 2019, 24 (3) : 1049-1077. doi: 10.3934/dcdsb.2019006
##### References:

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To Professor Valery Melnik, in Memoriam

##### References:
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