American Institute of Mathematical Sciences

Advanced
July  1998, 4(3): 455-466. doi: 10.3934/dcds.1998.4.455

Attractors for families of processes in weak topologies of Banach spaces

Filippo Gazzola 1, and  Mirko Sardella 2,

1. 

Dipartimento di Scienze T.A. - via Cavour 84, 15100 Alessandria, Italy
2. 

Dipartimento di Matematica del Politecnico, corso Duca degli Abruzzi 24, 10129 Torino, Italy

Received  January 1998 Published  April 1998

A general theory for the study of families of processes in the weak topology of some Banach space is suggested: sufficient conditions for the existence and connectedness of attractors are proved. The results apply to (nonlinear) nonautonomous evolution partial differential equations for which the behavior of the corresponding processes is better described when the phase space is endowed with its weak topology.
Keywords: Processes, compactification at infinity..
Mathematics Subject Classification: 47H20, 35B40, 35K5.
Citation: Filippo Gazzola, Mirko Sardella. Attractors for families of processes in weak topologies of Banach spaces. Discrete & Continuous Dynamical Systems - A, 1998, 4 (3) : 455-466. doi: 10.3934/dcds.1998.4.455
[1]

Richard Evan Schwartz. Outer billiards on the Penrose kite: Compactification and renormalization. Journal of Modern Dynamics, 2011, 5 (3) : 473-581. doi: 10.3934/jmd.2011.5.473
[2]

Ravi Vakil and Aleksey Zinger. A natural smooth compactification of the space of elliptic curves in projective space. Electronic Research Announcements, 2007, 13: 53-59.

[3]

Luis Barreira, Claudia Valls. Topological conjugacies and behavior at infinity. Communications on Pure & Applied Analysis, 2014, 13 (2) : 687-701. doi: 10.3934/cpaa.2014.13.687
[4]

Victor S. Kozyakin, Alexander M. Krasnosel’skii, Dmitrii I. Rachinskii. Arnold tongues for bifurcation from infinity. Discrete & Continuous Dynamical Systems - S, 2008, 1 (1) : 107-116. doi: 10.3934/dcdss.2008.1.107
[5]

Victor Kozyakin, Alexander M. Krasnosel’skii, Dmitrii Rachinskii. Asymptotics of the Arnold tongues in problems at infinity. Discrete & Continuous Dynamical Systems - A, 2008, 20 (4) : 989-1011. doi: 10.3934/dcds.2008.20.989
[6]

Erik Lindgren, Peter Lindqvist. Infinity-harmonic potentials and their streamlines. Discrete & Continuous Dynamical Systems - A, 2019, 39 (8) : 4731-4746. doi: 10.3934/dcds.2019192
[7]

Alexander Vladimirov. Equicontinuous sweeping processes. Discrete & Continuous Dynamical Systems - B, 2013, 18 (2) : 565-573. doi: 10.3934/dcdsb.2013.18.565
[8]

James Broda, Alexander Grigo, Nikola P. Petrov. Convergence rates for semistochastic processes. Discrete & Continuous Dynamical Systems - B, 2019, 24 (1) : 109-125. doi: 10.3934/dcdsb.2019001
[9]

Alexander Krasnosel'skii, Jean Mawhin. The index at infinity for some vector fields with oscillating nonlinearities. Discrete & Continuous Dynamical Systems - A, 2000, 6 (1) : 165-174. doi: 10.3934/dcds.2000.6.165
[10]

Michel Chipot, Aleksandar Mojsic, Prosenjit Roy. On some variational problems set on domains tending to infinity. Discrete & Continuous Dynamical Systems - A, 2016, 36 (7) : 3603-3621. doi: 10.3934/dcds.2016.36.3603
[11]

Guillaume James, Dmitry Pelinovsky. Breather continuation from infinity in nonlinear oscillator chains. Discrete & Continuous Dynamical Systems - A, 2012, 32 (5) : 1775-1799. doi: 10.3934/dcds.2012.32.1775
[12]

Yukihiro Seki. A remark on blow-up at space infinity. Conference Publications, 2009, 2009 (Special) : 691-696. doi: 10.3934/proc.2009.2009.691
[13]

Francesco Della Pietra, Ireneo Peral. Breaking of resonance for elliptic problems with strong degeneration at infinity. Communications on Pure & Applied Analysis, 2011, 10 (2) : 593-612. doi: 10.3934/cpaa.2011.10.593
[14]

Begoña Alarcón, Víctor Guíñez, Carlos Gutierrez. Hopf bifurcation at infinity for planar vector fields. Discrete & Continuous Dynamical Systems - A, 2007, 17 (2) : 247-258. doi: 10.3934/dcds.2007.17.247
[15]

Wael Bahsoun, Paweł Góra. SRB measures for certain Markov processes. Discrete & Continuous Dynamical Systems - A, 2011, 30 (1) : 17-37. doi: 10.3934/dcds.2011.30.17
[16]

Giuseppe Toscani. A kinetic description of mutation processes in bacteria. Kinetic & Related Models, 2013, 6 (4) : 1043-1055. doi: 10.3934/krm.2013.6.1043
[17]

Mathias Staudigl. A limit theorem for Markov decision processes. Journal of Dynamics & Games, 2014, 1 (4) : 639-659. doi: 10.3934/jdg.2014.1.639
[18]

Oliver Knill. A deterministic displacement theorem for Poisson processes. Electronic Research Announcements, 1997, 3: 110-113.

[19]

Jacek Banasiak. Transport processes with coagulation and strong fragmentation. Discrete & Continuous Dynamical Systems - B, 2012, 17 (2) : 445-472. doi: 10.3934/dcdsb.2012.17.445
[20]

Artur Stephan, Holger Stephan. Memory equations as reduced Markov processes. Discrete & Continuous Dynamical Systems - A, 2019, 39 (4) : 2133-2155. doi: 10.3934/dcds.2019089

2018 Impact Factor: 1.143

Tools

Metrics

  • PDF downloads (13)
  • HTML views (0)
  • Cited by (1)

Other articles
by authors

[Back to Top]

Copyright © 2019 American Institute of Mathematical Sciences