Abstract:

In this paper, we are concerned with the dynamical behavior of the nonclassical diffusion equations with fading memory and supercritical nonlinearity on unbounded domain ${{\mathbb{R}}^{n}}$. By applying semigroup theory and method of contractive function, we obtain the existence of global attractors in ${{H}^{1}}\left( {{\mathbb{R}}^{n}} \right)\times L_{\mu }^{2}\left( {{\mathbb{R}}^{+}};{{H}^{1}}\left( {{\mathbb{R}}^{n}} \right) \right)$, when the external forcing term g merely belongs to H^-1(${{\mathbb{R}}^{n}}$).

Key words: Nonclassical diffusion equation, Fading memory, Contractive function, Global attractor