Diagana, Toka On the existence of almost automorphic solutions to some abstract hyperbolic differential equations. (English) Zbl 1194.35274 Bull. Belg. Math. Soc. - Simon Stevin 17, No. 2, 219-234 (2010). 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 Keywords:sectorial operator; analytic semigroup; hyperbolic semigroup; almost automorphic function; heat equation with delay PDFBibTeX XMLCite \textit{T. Diagana}, Bull. Belg. Math. Soc. - Simon Stevin 17, No. 2, 219--234 (2010; Zbl 1194.35274) Full Text: Euclid