Abstract
In this work, we study the existence and uniqueness of almost automorphic solutions for semilinear nonautonomous parabolic evolution equations with inhomogeneous boundary conditions using the exponential dichotomy. We assume that the homogeneous problem satisfies the “Acquistapace–Terreni” conditions and that the forcing terms are Stepanov-like almost automorphic. An example is given for illustration.
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The authors would like to thank the referee for careful reading of the manuscript and useful suggestions.
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Communicated by Abdelaziz Rhandi.
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Baroun, M., Ezzinbi, K., Khalil, K. et al. Almost automorphic solutions for nonautonomous parabolic evolution equations. Semigroup Forum 99, 525–567 (2019). https://doi.org/10.1007/s00233-019-10045-w
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DOI: https://doi.org/10.1007/s00233-019-10045-w