American Institute of Mathematical Sciences

Advanced
July  2003, 9(4): 937-948. doi: 10.3934/dcds.2003.9.937

Spatially periodic equilibria for a non local evolution equation

Saulo R.M. Barros 1, , Antônio L. Pereira 1, , Cláudio Possani 1, and  Adilson Simonis 1,

1. 

Instituto de Matemática e Estatística, Universidade de São Paulo, R. do Matão 1010, 05508-900, S. Paulo, Brazil, Brazil, Brazil, Brazil

Received  November 2001 Revised  December 2002 Published  April 2003

In this work we prove the existence of a global attractor for the non local evolution equation $ \frac { \partial m ( r , t ) } { \partial t } = - m ( r , t ) + \tanh ( \beta J $*$ m ( r , t ) ) $ in the space of $\tau$-periodic functions, for $\tau$ sufficiently large. We also show the existence of non constant (unstable) equilibria in these spaces.
Keywords: Ising spin system, global attractor, numerical results., stationary solutions, periodic equilibria.
Mathematics Subject Classification: 45JO5, 45M05, 34C35, 34D4.
Citation: Saulo R.M. Barros, Antônio L. Pereira, Cláudio Possani, Adilson Simonis. Spatially periodic equilibria for a non local evolution equation. Discrete & Continuous Dynamical Systems - A, 2003, 9 (4) : 937-948. doi: 10.3934/dcds.2003.9.937
[1]

Zhirong He, Weinian Zhang. Critical periods of a periodic annulus linking to equilibria at infinity in a cubic system. Discrete & Continuous Dynamical Systems - A, 2009, 24 (3) : 841-854. doi: 10.3934/dcds.2009.24.841
[2]

Jérôme Coville, Juan Dávila. Existence of radial stationary solutions for a system in combustion theory. Discrete & Continuous Dynamical Systems - B, 2011, 16 (3) : 739-766. doi: 10.3934/dcdsb.2011.16.739
[3]

Sergiu Aizicovici, Hana Petzeltová. Convergence to equilibria of solutions to a conserved Phase-Field system with memory. Discrete & Continuous Dynamical Systems - S, 2009, 2 (1) : 1-16. doi: 10.3934/dcdss.2009.2.1
[4]

Marilena N. Poulou, Nikolaos M. Stavrakakis. Global attractor for a Klein-Gordon-Schrodinger type system. Conference Publications, 2007, 2007 (Special) : 844-854. doi: 10.3934/proc.2007.2007.844
[5]

Francesca Bucci, Igor Chueshov, Irena Lasiecka. Global attractor for a composite system of nonlinear wave and plate equations. Communications on Pure & Applied Analysis, 2007, 6 (1) : 113-140. doi: 10.3934/cpaa.2007.6.113
[6]

Olivier Goubet, Manal Hussein. Global attractor for the Davey-Stewartson system on $\mathbb R^2$. Communications on Pure & Applied Analysis, 2009, 8 (5) : 1555-1575. doi: 10.3934/cpaa.2009.8.1555
[7]

Daniel Ginsberg, Gideon Simpson. Analytical and numerical results on the positivity of steady state solutions of a thin film equation. Discrete & Continuous Dynamical Systems - B, 2013, 18 (5) : 1305-1321. doi: 10.3934/dcdsb.2013.18.1305
[8]

Caixia Chen, Shu Wen. Wave breaking phenomena and global solutions for a generalized periodic two-component Camassa-Holm system. Discrete & Continuous Dynamical Systems - A, 2012, 32 (10) : 3459-3484. doi: 10.3934/dcds.2012.32.3459
[9]

Ning Ju. The global attractor for the solutions to the 3D viscous primitive equations. Discrete & Continuous Dynamical Systems - A, 2007, 17 (1) : 159-179. doi: 10.3934/dcds.2007.17.159
[10]

Carlos J. Garcia-Cervera, Xiao-Ping Wang. Spin-polarized transport: Existence of weak solutions. Discrete & Continuous Dynamical Systems - B, 2007, 7 (1) : 87-100. doi: 10.3934/dcdsb.2007.7.87
[11]

Yukio Kan-On. Global bifurcation structure of stationary solutions for a Lotka-Volterra competition model. Discrete & Continuous Dynamical Systems - A, 2002, 8 (1) : 147-162. doi: 10.3934/dcds.2002.8.147
[12]

V. Barbu. Periodic solutions to unbounded Hamiltonian system. Discrete & Continuous Dynamical Systems - A, 1995, 1 (2) : 277-283. doi: 10.3934/dcds.1995.1.277
[13]

M. Grasselli, Hana Petzeltová, Giulio Schimperna. Convergence to stationary solutions for a parabolic-hyperbolic phase-field system. Communications on Pure & Applied Analysis, 2006, 5 (4) : 827-838. doi: 10.3934/cpaa.2006.5.827
[14]

Francesco Paparella, Alessandro Portaluri. Geometry of stationary solutions for a system of vortex filaments: A dynamical approach. Discrete & Continuous Dynamical Systems - A, 2013, 33 (7) : 3011-3042. doi: 10.3934/dcds.2013.33.3011
[15]

Luca Battaglia. A general existence result for stationary solutions to the Keller-Segel system. Discrete & Continuous Dynamical Systems - A, 2019, 39 (2) : 905-926. doi: 10.3934/dcds.2019038
[16]

Alan Elcrat, Ray Treinen. Numerical results for floating drops. Conference Publications, 2005, 2005 (Special) : 241-249. doi: 10.3934/proc.2005.2005.241
[17]

Sabri Bensid, Jesús Ildefonso Díaz. Stability results for discontinuous nonlinear elliptic and parabolic problems with a S-shaped bifurcation branch of stationary solutions. Discrete & Continuous Dynamical Systems - B, 2017, 22 (5) : 1757-1778. doi: 10.3934/dcdsb.2017105
[18]

Yuxiang Zhang, Shiwang Ma. Some existence results on periodic and subharmonic solutions of ordinary $P$-Laplacian systems. Discrete & Continuous Dynamical Systems - B, 2009, 12 (1) : 251-260. doi: 10.3934/dcdsb.2009.12.251
[19]

Zhiming Guo, Xiaomin Zhang. Multiplicity results for periodic solutions to a class of second order delay differential equations. Communications on Pure & Applied Analysis, 2010, 9 (6) : 1529-1542. doi: 10.3934/cpaa.2010.9.1529
[20]

Fethallah Benmansour, Guillaume Carlier, Gabriel Peyré, Filippo Santambrogio. Numerical approximation of continuous traffic congestion equilibria. Networks & Heterogeneous Media, 2009, 4 (3) : 605-623. doi: 10.3934/nhm.2009.4.605

2018 Impact Factor: 1.143

Tools

Metrics

  • PDF downloads (9)
  • HTML views (0)
  • Cited by (6)

Other articles
by authors

[Back to Top]

Copyright © 2019 American Institute of Mathematical Sciences