Positive irreducible semigroups and their long-time behaviour
2020 ◽
Vol 378
(2185)
◽
pp. 20190611
Keyword(s):
The notion Perron–Frobenius theory usually refers to the interaction between three properties of operator semigroups: positivity, spectrum and long-time behaviour. These interactions gives rise to a profound theory with plenty of applications. By a brief walk-through of the field and with many examples, we highlight two aspects of the subject, both related to the long-time behaviour of semigroups: (i) The classical question how positivity of a semigroup can be used to prove convergence to an equilibrium as t → ∞. (ii) The more recent phenomenon that positivity itself sometimes occurs only for large t , while being absent for smaller times. This article is part of the theme issue ‘Semigroup applications everywhere’.
2011 ◽
Vol 4
(2)
◽
pp. 273-309
◽
Keyword(s):
2002 ◽
Vol 18
(3)
◽
pp. 579-596
◽
2006 ◽
Vol 18
(14)
◽
pp. S235-S243
◽
Keyword(s):
2006 ◽
Vol 15
(4)
◽
pp. 1119-1135
◽
2011 ◽
Vol 648
(1)
◽
pp. 132-138
◽
Keyword(s):
2004 ◽
Vol 15
(1)
◽
pp. 55-77
◽