Attractor and dimension for discretization of a damped wave equation with periodic nonlinearity

Shengfan Zhou

DOI: http://dx.doi.org/10.12775/TMNA.2000.020

Abstract


The existence and Hausdorff dimension of the global attractor for
discretization of a damped wave equation with the periodic nonlinearity
under the periodic boundary conditions are studied for any space
dimension. The obtained Hausdorff dimension is independent of the mesh
sizes and the space dimension and remains small for large damping, which
conforms to the physics.

Keywords


Wave equation; finite difference; global attractor; Hausdorff dimension

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