FINITE DIMENSIONALITY OF GLOBAL ATTRACTORS FOR A NONCLASSICAL DIFFUSION EQUATION LACKING INSTANTANEOUS DAMPING WITH MEMORY
Abstract
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.
điểm /
đánh giá
Published
2024-03-03
Section
Bài viết