Absolute and convective stability in large domainsBj
نویسنده
چکیده
Existence and stability of travelling waves are conveniently studied on unbounded domains , for instance, on the real line. Motivated by numerical and experimental studies, we investigate the eeects of truncating the unbounded domain to a large but bounded domain. It is shown that periodic boundary conditions accurately reproduce the L 2-spectrum of the unbounded domain, whereas separated boundary conditions introduce two new phenomena: Firstly, the essential spectrum is in general shifted to the so-called absolute spectrum that corresponds to optimally chosen exponential weights on the unbounded domain. Secondly, separated boundary conditions may generate additional eigenvalues.
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