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On the existence of almost automorphic solutions to some abstract hyperbolic differential equations. (English) Zbl 1194.35274

Summary: We give some sufficient conditions, which do ensure the existence and uniqueness of a compact almost automorphic solution to some hyperbolic differential equations. As an illustration, we study the existence and uniqueness of almost automorphic solutions to a one-dimensional heat equation with small delays.

MSC:

35L90 Abstract hyperbolic equations
44A35 Convolution as an integral transform
42A85 Convolution, factorization for one variable harmonic analysis
42A75 Classical almost periodic functions, mean periodic functions
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Full Text: Euclid