Advances in Differential Equations

Singular integro-differential equations of parabolic type

Angelo Favini, Alfredo Lorenzi, and Hiroki Tanabe

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Abstract

We study a linear singular first-order integro-differential Cauchy problems in Banach spaces. Singular here means that the integro differential equation is not in normal form neither can it be reduced to such a form. We generalize to this context some existence and uniqueness theorems known for differential equations. Particular attention is given to single out the optimal regularity properties of solutions as well as to point out several explicit applications related to singular partial integro-differential of parabolic type.

Article information

Source
Adv. Differential Equations Volume 7, Number 7 (2002), 769-798.

Dates
First available in Project Euclid: 27 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.ade/1356651705

Mathematical Reviews number (MathSciNet)
MR1895165

Zentralblatt MATH identifier
1033.45010

Subjects
Primary: 34K30: Equations in abstract spaces [See also 34Gxx, 35R09, 35R10, 47Jxx]
Secondary: 35K90: Abstract parabolic equations 35R10: Partial functional-differential equations 45J05: Integro-ordinary differential equations [See also 34K05, 34K30, 47G20] 49N20: Periodic optimization

Citation

Favini, Angelo; Lorenzi, Alfredo; Tanabe, Hiroki. Singular integro-differential equations of parabolic type. Adv. Differential Equations 7 (2002), no. 7, 769--798. https://projecteuclid.org/euclid.ade/1356651705.


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