Abstract and Applied Analysis

Almost periodic mild solutions of a class of partial functional differential equations

Bernd Aulbach and Nguyen Van Minh

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Abstract

We study the existence of almost periodic mild solutions of a class of partial functional differential equations via semilinear almost periodic abstract functional differential equations of the form (*)x=f(t,x,xt). To this end, we first associate with every almost periodic semilinear equation (**)x=F(t,x). a nonlinear semigroup in the space of almost periodic functions. We then give sufficient conditions (in terms of the accretiveness of the generator of this semigroup) for the existence of almost periodic mild solutions of (**) as fixed points of the semigroup. Those results are then carried over to equation (*). The main results are stated under accretiveness conditions of the function f in terms of x and Lipschitz conditions with respect to xt.

Article information

Source
Abstr. Appl. Anal., Volume 3, Number 3-4 (1998), 425-436.

Dates
First available in Project Euclid: 8 April 2003

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1049832735

Digital Object Identifier
doi:10.1155/S1085337598000645

Mathematical Reviews number (MathSciNet)
MR1749420

Zentralblatt MATH identifier
0981.34064

Subjects
Primary: 34K30: Equations in abstract spaces [See also 34Gxx, 35R09, 35R10, 47Jxx] 35R10: Partial functional-differential equations 35B15: Almost and pseudo-almost periodic solutions
Secondary: 47H20: Semigroups of nonlinear operators [See also 37L05, 47J35, 54H15, 58D07]

Keywords
Almost periodic solutions partial functional differential equations semilinear equations semigroups of nonlinear operators accretiveness

Citation

Aulbach, Bernd; Minh, Nguyen Van. Almost periodic mild solutions of a class of partial functional differential equations. Abstr. Appl. Anal. 3 (1998), no. 3-4, 425--436. doi:10.1155/S1085337598000645. https://projecteuclid.org/euclid.aaa/1049832735


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