Autonomous and non-autonomous attractors for differential equations with delays

By Tomás Caraballo, Pedro Marín-Rubio, José Valero. 2005

114 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computer Networks and Communications, Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/088ffb680ac84fef6e327999ae8a58ceaf3aef2a

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In Applied Mathematics

In Computer Networks and Communications

In Control and Systems Engineering

Citations in the corpus

Pullback attractors for 2D-Navier-Stokes equations with delays in continuous and sub-linear operators (2009, background): “We recall that some sort of results for the combination of these ingredients appear in [6, 7] but not completely adapted to the sharp conditions involving a family depending on time.”
Synchronization analysis of linearly coupled systems described by differential equations with a coupling delay (2006, background): “This proposition comes from theorem 18 in [37] and the proof will be given in Appendix 1.”
A survey on Navier-Stokes models with delays: Existence, uniqueness and asymptotic behavior of solutions (2015, background): “, when one wishes to do it under a general functional formulation (see [8] for more details).”
Attractors for differential equations with unbounded delays (2007, methodology): “[9]), just using concatenation and translation of solutions to (3), that U is a strict MDP.”
Attractors for reaction-diffusion equations in R N with continuous nonlinearity (2005, background): “Several results concerning the existence of global attractors in the case of nonuniqueness have been proved for differential inclusions (see [25,31,32]), reaction–diffusion equations (see [15,17,23]), parabolic problems (see [13,45]), phase-field equations (see [22,24]), wave equations (see [7,16]),”
Kernel sections and uniform attractors of multi-valued semiprocesses☆ (2007, background): “Autonomous set-valued dynamical systems and their attractors have been extensively studied in mathematical literature, especially in the recent years (see, for example, [1,3,6,7,12,14,16, 18,21,22,30] and the references cited therein).”
On the connectedness and asymptotic behaviour of solutions of reaction–diffusion systems☆ (2006, background): “In the last years several results concerning attractors in the case of equations without uniqueness have been obtained for differential inclusions [20,24,25], parabolic problems [8,34], phase-field equations [16,18], wave equations [3,10], the three-dimensional Navier–Stokes equation [2,4,5,10,28,30”