Absolute and convective stability in large domains
Björn Sandstede, Arnd Scheel · 2000
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 effects of truncating the unbounded domain to a large but bounded domain. It is shown that periodic boundary conditions accurately reproduce the L²-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.