On the dimension of the global attractor for a damped semilinear wave equation with critical exponent

Journal of Mathematical Physics

Volumn 41, Issue 7, 2000, Pages 4957-4966

  Huang, Yu ^a   Yi, Zhao ^a   Yin, Zhaoyang ^a  

^a SUN YAT SEN UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034374595     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.533386     Document Type: Article

References (8)

1. R. Temam, Infinite-dimensional Dynamical Systems in Mechanics and Physics, 2nd ed., Applied Math. Sci., Vol. 68 (Spring-Verlag, New York, 1997).
2. J. Arrieta, A. Carvalho, and J. K. Hale, "A damped equation with critical exponent," Commun. Partial Diff. Eqns. 17, 841-866 (1992).
3. A. V. Babin and M. I. Vishik, Attractors of Evolution Equations, Studies in Math, and Its Applications Vol. 25 (North-Holland, New York, 1992).
4. Y. Huang, "Estimate of the Hausdorff and fractal dimensions of the global attractors for nonlinear wave equations with damping," Acta Matematicae Applicatae Sinica 21, 257-266 (1998).
5. Z. Shengfan, "On dimension of the global attractor for damped nonlinear wave equations," J. Math. Phys. 40, 1432-1438 (1999).
6. J. L. Lions and E. Magenes, Non-homogenous Boundary Value Problems and Applications (Spring-Verlag, New York, 1972).
7. E. Feireisl and E. Zuazua, "Global attractors for semilinear wave equations with locally distributed nonlinear damping and critical exponent," Commun. Partial Diff. Eqns. 18, 1539-1555 (1993).
8. Z. Shengfan, "Dimension of the global attractor for damped semilinear wave equations with critical exponent," J. Math. Phys. 40, 4444-4451 (1999).