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Asymptotical dynamics of Selkov equations. (English) Zbl 1161.37347

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.

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)
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