FINITE DIMENSIONALITY OF GLOBAL ATTRACTORS FOR A NONCLASSICAL DIFFUSION EQUATION LACKING INSTANTANEOUS DAMPING WITH MEMORY
Từ khóa:
Non-classical diffusion equation; lacking instantaneous damping; memory; global attractor; fractal dimension.
Tóm tắt
We consider a periodic boundary value problem for a
nonclassical diffusion equation lacking instantaneous damping with hereditary
memory 0 1
0
u u s u t s ds k u u g t t ( ) ( ) | | . p
- - - + = -
The main feature of the model is that the equation does not contain a term of
the form -u , which contributes to an instantaneous damping. Setting the
problem in the history framework, we prove that the global attractor generated
by the above-mentioned nonclassical diffusion equation is finite dimensional.
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Phát hành ngày
2024-03-03
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