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Existence and uniqueness of pseudo almost periodic solutions to some abstract partial neutral functional-differential equations and applications. (English) Zbl 1123.34060
The authors consider the existence and uniqueness of pseudo almost periodic (mild) solutions to some classes of first-order partial neutral functional-differential equations. Under suitable assumptions, existence and uniqueness results are obtained. Applications include both a partial integro-differential equation arising in control systems and a scalar reaction-diffusion equation with delay.

MSC:
34K30Functional-differential equations in abstract spaces
35R10Partial functional-differential equations
45K05Integro-partial differential equations