ISSN:
1432-0673
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
,
Physics
Notes:
Abstract For scalar equations $$u_t = u_{xx} + f(x, u, u_x )$$ with x ε S 1 and f ε C 2 we show that the classical theorem of Poincaré and Bendixson holds: the ω-limit set of any bounded solution satisfies exactly one of the following alternatives: - it consists in precisely one periodic solution, or - it consists of solutions tending to equilibrium as $$t \to \pm \infty $$ This is surprising, because the system is genuinely infinite-dimensional.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00251553