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Dimensional estimate of global attractor for nonlinear parabolic equations

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1 Author(s)
Celi, Gao ; Department of Applied Mathematics, Tsinghua University, Beijing 100084

The nonlinear parabolic equation u_{t} = \Delta a (u) + f (u) with initial and Dirichlet boundary conditions is considered in the paper. Under the condition that a(u) is nondegenerate, the semigroup is proved to be Fréchet differentiable; Estimates of soutions of the linear variation equation prove that the Hausdorff and fractal dimensions of the equation's global attractor are finite.

Published in:

Tsinghua Science and Technology  (Volume:1 ,  Issue: 3 )