Finite dimensional behavior of periodic and asymptotically periodic processes

Nonlinear Analysis, Theory, Methods and Applications

Volumn 28, Issue 11, 1997, Pages 1785-1797

  Shuhong, Fang ^a  

^a FUDAN UNIVERSITY   (China)

Author keywords

Asymptotically periodic processes; Dimension; Global attractor; Periodic process; Uniform attractor

Indexed keywords

ASYMPTOTIC STABILITY; BOUNDARY VALUE PROBLEMS; DIFFERENTIAL EQUATIONS; EIGENVALUES AND EIGENFUNCTIONS; FINITE DIFFERENCE METHOD; MATHEMATICAL OPERATORS; NAVIER STOKES EQUATIONS;

FINITE DIMENSIONAL BEHAVIOR; FINITE FRACTAL DIMENSION; GLOBAL ATTRACTOR; GRONWALL INEQUALITY; HOLDER CONTINUITY; PERIODIC PROCESSES; UNIFORM ATTRACTOR;

NONLINEAR EQUATIONS;

EID: 0031165131     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0362-546X(95)00229-O     Document Type: Article

References (12)

1. GHIDAGLIA J. M. & TEMAN R., Attractors for damped nonlinear hyperbolic equations, J. Math. pures appl. 66, 273-319 (1987).
2. GHIDAGLIA J. M. & TEMAN R., Periodic dynamical systems with application to sine-Gordon equations: estimates on the fractal dimension of the universal attractor, Contemp. Math. Amer. Soc. 99, 223-249 (1989).
3. SHUHONG FANG, Global attractor for general nonautonomous dynamical systems, Nonlinear World 2, 191-216 (1995).
4. HARAUX A., Attracts of asymptotically compact processes and applications to nonlinear partial differential equations, Communs partial diff. Eqns 13, 1384-1414 (1988).
5. SHUHONG FANG, Finite dimensional behavior of nonautonomous dynamical systems with application to the forced oscillations of an extensible bean, Dynamics of Continuous, Discrete and Impulsive Systems 1, 163-176 (1995).
6. FEIREIS E., Finite-dimensional behavior of a nonautonomous partial differential equation: forced oscillations of an extensible beam, J. diff. Eqns 101, 302-312 (1993).
7. CHEPYZHOV V. V. & VISHIK M. I., Attractors of nonautonomous dynamical systems and their dimension, J. math. pures appl. 73, 279-333 (1994).
8. FALCONER K. J., Fractal Geometry, Mathematical Foundations and Applications. Wiley, New York (1990).
9. CONSTANTIN P. & FOIAS C., Navier-Stokes Equations. University of Chicago Press, Chicago (1988).
10. TEMAM R., Navier-Stokes Equations, Theory and Numerical Analysis, Revised Edition. North-Holland (1984).
11. LOINS J. L., Quelques Methods de Résolution des Problémes aux Limites Non Linéares. Dunod, Paris (1969).
12. TEMAM R., Infinite Dimensional Dynamical Systems in Mechanics and Physics. Springer, New York (1988).