Differential and Integral Equations

Partial functional differential equations with nonautonomous past in {$L^p$}-phase spaces

Genni Fragnelli and Gregor Nickel

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We prove the equivalence of the well-posedness of a partial differential equation with nonautonomous past and an associated abstract Cauchy problem. This equivalence is then used to derive sufficient conditions for exponential stability of the solutions.

Article information

Differential Integral Equations, Volume 16, Number 3 (2003), 327-348.

First available in Project Euclid: 21 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 34K30: Equations in abstract spaces [See also 34Gxx, 35R09, 35R10, 47Jxx]
Secondary: 35K90: Abstract parabolic equations 35R10: Partial functional-differential equations 47D06: One-parameter semigroups and linear evolution equations [See also 34G10, 34K30]


Fragnelli, Genni; Nickel, Gregor. Partial functional differential equations with nonautonomous past in {$L^p$}-phase spaces. Differential Integral Equations 16 (2003), no. 3, 327--348. https://projecteuclid.org/euclid.die/1356060674

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