Pointwise asymptotic behavior of modulated periodic reaction–diffusion waves

Modulated periodic stokes waves in deep water

Modulated deep-water 1D Stokes waves are considered experimentally and theoretically. Wave trains are modulated in a controlled fashion and their evolution is recorded. Data from repeated laboratory experiments are reproducible near the wave maker, but diverge away from the wave maker. Numerical integration of a perturbed nonlinear Schrodinger equation and an associated linear spectral problem ...

Asymptotic Behavior for Asymptotically Periodic

The properties of ω-limit set and global asymptotic behavior are first obtained for asymptotically autonomous discrete dynamical processes on metric spaces.Then certain equivalence of the asymptotic behavior between an asymptotically periodic semiflows and its associated asymptotically autonomous discrete dynamical process is proved. As some applications, the global behavior of asymptotically p...

Asymptotic Behavior of a Periodic Diffusion System

On the Asymptotic Behavior of Ascending Waves

Ramsey theory has been described in many ways. Weisteinn [1] defines Ramsey theory broadly as “the study of combinatorial objects in which a certain degree of order must occur as the scale of the object becomes large.” It is the diversity of results considered to be those of Ramsey theory that requires this and any all-encompassing definition to be so vague. For this reason, Landman and Roberts...

Asymptotic Behavior of Solutions of a Periodic Diffusion Equation

We consider a degenerate parabolic equation with logistic periodic sources. First, we establish the existence of nontrivial nonnegative periodic solutions by monotonicity method. Then by using Moser iterative technique and the method of contradiction, we establish the boundedness estimate of nonnegative periodic solutions, by which we show that the attraction of nontrivial nonnegative periodic ...