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Global attractors for a nonclassical diffusion equation. (English) Zbl 1128.35027

Summary: We prove the existence of global attractors in ${H}_{0}^{1}\left({\Omega }\right)$ for a nonclassical diffusion equation

${u}_{t}-{\Delta }{u}_{t}-{\Delta }u=f\left(u\right)+{D}_{i}{f}^{i}+g\left(x\right)\phantom{\rule{1.em}{0ex}}\text{in}\phantom{\rule{4.pt}{0ex}}{\Omega }·$

Two types of nonlinearity $f$ are considered: one is the critical exponent, and the other is the polynomial growth of arbitrary order.

##### MSC:
 35B41 Attractors (PDE) 35Q35 PDEs in connection with fluid mechanics 35B40 Asymptotic behavior of solutions of PDE
##### Keywords:
existence of global attractors; critical exponent
##### References:
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