The attractor for a nonlinear reaction-diffusion system in the unbounded domain and Kolmogorov's \(\varepsilon\)-entropy (Q2774476)

This paper is devoted to the second order parabolic equations and systems of a reaction-diffusion type of the form NEWLINE\[NEWLINE\partial_t u=\Delta_xu-f(u)- \lambda_0 u+g(t),\;u|_{t=0}=u_0,\;u|_{\partial \Omega}=0,NEWLINE\]NEWLINE where \(\Omega\subset \mathbb{R}^n\) is an unbounded domain, \(\lambda_0>0\). Under some dissipative assumptions on \(f\) the author shows the existence of a global attractor in the corresponding local topology. Since in this case fractal dimension of the invariant set is not a relevant characteristic, he replaces this characteristic by Kolmogorov's \(\varepsilon\)-entropy. He presents upper and lower bounds of Kolmogorov's \(\varepsilon\)-entropy of the attractors.