2019-03-112019-03-112019-03Caballero Toro, R., Carvalho, A.N., Marín Rubio, P. y Valero Cuadra, J. (2019). Robustness of dynamically gradient multivalued dynamical systems. Discrete and Continuous Dynamical Systems - Series B, 24 (3), 1049-1077.1531-34921553-524Xhttps://hdl.handle.net/11441/84141In 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.application/pdfengAttribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/AttractorsReaction-diffusion equationsStabilityDynamically gradient multivalued semiflowsMorse decompositionSet-valued dynamical systemsinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/openAccess10.3934/dcdsb.2019006