Almost automorphic solutions for some evolution equations through the minimizing for some subvariant functional, applications to heat and wave equations with nonlinearities |
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Authors: | Philippe Cieutat |
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Institution: | a Laboratoire de Mathématiques, Université Versailles-Saint-Quentin-en-Yvelines, 45 avenue des États-Unis, 78035 Versailles cedex, France b Université Cadi Ayyad, Faculté des Sciences Semlalia, Département de Mathématiques, B.P. 2390, Marrakech, Morocco |
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Abstract: | In this work, we study the existence of bounded and almost automorphic solutions for evolution equations in Banach spaces. We suppose that the linear part is the infinitesimal generator of a compact C0-semigroup of bounded linear operators and the nonlinear part is an almost automorphic function with respect to the second argument. We give sufficient conditions ensuring the existence of an almost automorphic solution when there is at least one bounded solution on R+. We use the subvariant functional method to show that every K-minimizing mild solution is compact almost automorphic. Applications are provided for both heat and wave equations with nonlinearities in several functional spaces. |
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Keywords: | Bounded solution K-mild solution Almost automorphic solution Evolution equations Semigroup Compact operator Heat and wave equations |
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