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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Abstract

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

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

Dates
First available in Project Euclid: 21 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356060674

Mathematical Reviews number (MathSciNet)
MR1947956

Zentralblatt MATH identifier
1044.34038

Subjects
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]

Citation

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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