Eventually positive semigroups of linear operators (Q499232)

The authors consider strongly continuous semigroups of operator \(e^{tA}\), \(t\geq 0\), on ordered Banach lattices, mostly function spaces. As they note, the semigroups generated by many differential operators need not be positive. However, it is possible to relax the definition of ``positiveness'' and still obtain remarkable results. The semigroup \(e^{tA} \) is called eventually positive, if \(e^{tA} u\) is positive for large enough \(t\) whenever \(u>0\). This condition is described also in terms of resolvents. The authors give several interesting examples of eventually positive semigroups generated by differential operators, including fourth order elliptic operators.