Local existence and global continuation for some partial functional integrodifferential equations. (English) Zbl 1246.34074

Ezzinbi, K.; Ghnimi, S.

Afr. Diaspora J. Math. 12, No. 1, 34-45 (2011).

Summary: We study the local existence of mild solutions for some partial functional integrodifferential equations. We suppose that the linear part has a resolvent operator. The nonlinear part is assumed to be continuous. The solution may blow up in finite time. An application is provided to illustration.

MSC:

34K30	Functional-differential equations in abstract spaces
34K40	Neutral functional-differential equations
47D06	One-parameter semigroups and linear evolution equations
45K05	Integro-partial differential equations
47N20	Applications of operator theory to differential and integral equations

Keywords:

partial functional integrodifferential equations; Schauder fixed point theorem; compact resolvent operator; mild solutions