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- W1965469200 abstract "We show that a strongly continuous operator semigroup can be associated with the functional differential delay equation (FDE) [ left { {begin {array}{*{20}{c}} {xprime (t) + ax(t) + Bx(t) backepsilon F({x_t}),} hfill & {t geq 0} hfill {x{|_{{mathbb {R}^ - }}} = varphi in E} hfill & {} hfill end {array} } right .] under local conditions which give wide latitude to those subsets of the state space $X$ and initial data space $E$, respectively, where (a) the (generally multivalued) operator $B subseteq X times X$ is defined and accretive, and (b) the historyresponsive function $F:D(F) subseteq E to X$ is defined and Lipschitz continuous. The associated semigroup is then used to investigate existence and uniqueness of solutions to (FDE). By allowing the domain of the solution semigroup to be restricted according to specific local properties of $B$ and $F$, moreover, our methods automatically lead to assertions on flow invariance. We illustrate our results through applications to the Goodwin oscillator and a single species population model." @default.
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- W1965469200 title "Operator semigroups for functional-differential equations with delay" @default.
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- W1965469200 doi "https://doi.org/10.1090/s0002-9947-1994-1214785-x" @default.
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