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Almost automorphic solutions to some classes of partial evolution equations. (English) Zbl 1169.35300

Summary: We give in this work some sufficient conditions for the existence and uniqueness of almost automorphic (mild) solutions to some classes of partial evolution equations. Then we use our abstract results to discuss the existence and uniqueness of almost automorphic solutions to some partial differential equations.

MSC:

35A05 General existence and uniqueness theorems (PDE) (MSC2000)
34G20 Nonlinear differential equations in abstract spaces
47D06 One-parameter semigroups and linear evolution equations
47J35 Nonlinear evolution equations
35K60 Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations
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References:

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