You, Yuncheng Asymptotical dynamics of Selkov equations. (English) Zbl 1161.37347 Discrete Contin. Dyn. Syst., Ser. S 2, No. 1, 193-219 (2009). Summary: The existence of a global attractor for the solution semiflow of Selkov equations with Neumann boundary conditions on a bounded domain in space dimension \(n\leq 3\) is proved. This reaction-diffusion system features the oppositely-signed nonlinear terms so that the dissipative sign-condition is not satisfied. The asymptotical compactness is shown by a new decomposition method. It is also proved that the Hausdorff dimension and fractal dimension of the global attractor are finite. Cited in 16 Documents MSC: 37L30 Attractors and their dimensions, Lyapunov exponents for infinite-dimensional dissipative dynamical systems 35B40 Asymptotic behavior of solutions to PDEs 35B41 Attractors 35K55 Nonlinear parabolic equations 35K57 Reaction-diffusion equations 35Q80 Applications of PDE in areas other than physics (MSC2000) Keywords:Selkov equation; asymptotical dynamics; global attractor; absorbing set; asymptotic compactness; fractal dimension PDFBibTeX XMLCite \textit{Y. You}, Discrete Contin. Dyn. Syst., Ser. S 2, No. 1, 193--219 (2009; Zbl 1161.37347) Full Text: DOI