Differential and Integral Equations

Well-posedness and flow invariance for semilinear functional differential equations governed by non-densely defined operators

Hiroki Sano and Naoki Tanaka

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Abstract

The well-posedness and the flow invariance are studied for a semilinear functional differential equation governed by a family of non-densely defined operators in a general Banach space. The notion of mild solutions is introduced through a new type of variation of constants formula and the well-posedness is established under a semilinear stability condition with respect to a metric-like functional and a subtangential condition. The abstract result is applied to a size-structured model with birth delay.

Article information

Source
Differential Integral Equations, Volume 30, Number 9/10 (2017), 695-734.

Dates
First available in Project Euclid: 27 May 2017

Permanent link to this document
https://projecteuclid.org/euclid.die/1495850424

Mathematical Reviews number (MathSciNet)
MR3656484

Zentralblatt MATH identifier
06770139

Subjects
Primary: 34K30: Equations in abstract spaces [See also 34Gxx, 35R09, 35R10, 47Jxx] 47J35: Nonlinear evolution equations [See also 34G20, 35K90, 35L90, 35Qxx, 35R20, 37Kxx, 37Lxx, 47H20, 58D25] 34G20: Nonlinear equations [See also 47Hxx, 47Jxx]

Citation

Sano, Hiroki; Tanaka, Naoki. Well-posedness and flow invariance for semilinear functional differential equations governed by non-densely defined operators. Differential Integral Equations 30 (2017), no. 9/10, 695--734. https://projecteuclid.org/euclid.die/1495850424


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