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The nonclassical diffusion equation with hereditary memory $$\begin{aligned} u_t-\Delta u_t-\Delta u-\int _0^\infty \kappa (s)\Delta u(t-s)\,\mathrm{d}s +\varphi (u)=f \end{aligned}$$ u t - Δ u t - Δ u - ∫ 0 ∞ κ ( s ) Δ u ( t - s ) d s + φ ( u ) = f on a 3D bounded domain is considered, for a very general class of memory kernels $$\kappa $$ κ . Setting the problem both in the classical past history framework and in the more recent minimal state one, the related solution semigroups are shown to possess finite-dimensional regular exponential attractors.
Applied Mathematics and Optimization – Springer Journals
Published: Feb 1, 2016
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