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DISCRETE AND CONTINUOUS doi:10.3934/dcds.2009.25.1109 DYNAMICAL SYSTEMS
 

Summary: DISCRETE AND CONTINUOUS doi:10.3934/dcds.2009.25.1109
DYNAMICAL SYSTEMS
Volume 25, Number 4, December 2009 pp. 1109­1128
ASYMPTOTIC EQUIVALENCE AND KOBAYASHI-TYPE
ESTIMATES FOR NONAUTONOMOUS MONOTONE
OPERATORS IN BANACH SPACES
Felipe Alvarez
Departamento de Ingenier´ia Matem´atica, Centro de Modelamiento Matem´atico (CNRS UMI 2807)
Universidad de Chile, Blanco Encalada 2120, Santiago, Chile
Juan Peypouquet
Departamento de Matem´atica, Universidad T´ecnica Federico Santa Mar´ia
Av. Espa~na 1680, Valpara´iso, Chile
(Communicated by Mitsuharu Otani)
Abstract. We provide a sharp generalization to the nonautonomous case of
the well-known Kobayashi estimate for proximal iterates associated with max-
imal monotone operators. We then derive a bound for the distance between a
continuous-in-time trajectory, namely the solution to the differential inclusion
x + A(t)x 0, and the corresponding proximal iterations. We also establish
continuity properties with respect to time of the nonautonomous flow under
simple assumptions by revealing their link with the function t A(t). More-

  

Source: Alvarez, Felipe - Departamento de Ingeniería Matemática, Universidad de Chile

 

Collections: Mathematics; Engineering