FINITE DIMENSIONALITY OF GLOBAL ATTRACTORS FOR A NONCLASSICAL DIFFUSION EQUATION LACKING INSTANTANEOUS DAMPING WITH MEMORY

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.