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

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
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Full Text: Euclid