Convergence in smooth strongly monotone flows defined by semilinear parabolic equations. (English) Zbl 0684.34064

After the experimental discovery of oscillatory evolutions in processes described by parabolic systems, two approaches have been used to determine asymptotic properties of the corresponding flows: linearization near known equilibria, and imposition of ‘suitable’ smoothness conditions on the form of equations, allowing a comparison argument in a ‘suitable’ space. The author uses the latter approach to establish an order relation for bounded trajectories, but cannot dispense with linearizations. Although the number of hypotheses and restrictions is quite large, the author claims that they apply to models of experimental processes. This claim is not substantiated by a comparison of ‘suitable’ and realistic spaces.
Reviewer: I.Gumowski


34G99 Differential equations in abstract spaces
34A34 Nonlinear ordinary differential equations and systems
35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs
35B40 Asymptotic behavior of solutions to PDEs
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