On the evolution operator for abstract parabolic equations

1987 ◽  
Vol 60 (3) ◽  
pp. 281-314 ◽  
Author(s):  
Alessandra Lunardi
Keyword(s):  
Parabolic Equations ◽  
Evolution Operator ◽  
Abstract Parabolic Equations

Bounded solutions of linear periodic abstract parabolic equations

1988 ◽  
Vol 110 (1-2) ◽  
pp. 135-159 ◽  
Author(s):  
Alessandra Lunardi
Keyword(s):  
Banach Space ◽  
Parabolic Equations ◽  
Evolution Operator ◽  
Maximal Regularity ◽  
Analytic Semigroups ◽  
Bounded Solutions ◽  
Time Intervals ◽  
Abstract Parabolic Equations ◽  
Regularity Results ◽  
General Banach Space

SynopsisWe study the asymptotic behaviour of the parabolic evolution operatorG(t,s) associated with a family of generators of analytic semigroups {A(t);t∊ ℝ} in general Banach space, under the periodicity assumptionA(t) =A(t+T). We find new maximal regularity results for the bounded solutions of abstract nonhomogeneous parabolic equations in unbounded time intervals.

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