Almost automorphic solutions for some evolution equations through the minimizing for some subvariant functional, applications to heat and wave equations with nonlinearities

作者：Cieutat Philippe; Ezzinbi Khalil^*

来源：Journal of Functional Analysis, 2011, 260(9): 2598-2634.

DOI：10.1016/j.jfa.2011.01.002

• Bounded solution
• K-mild solution
• Almost automorphic solution
• Evolution equations
• Semigroup
• Compact operator
• Heat and wave equations

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 C-0-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.

• 出版日期2011-5-1