2020/05/27 by Dianda, Abdoul Aziz Kalifa, Ezzinbi, Khalil, Khalil, Kamal
#Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA) #Primary 46T20-47J35 #Secondary 34C27-35K58
paper · doi:10.48550/arxiv.2005.13442
In this work, we prove the existence and uniqueness of μ-pseudo almost automorphic solutions for some class of semilinear nonautonomous evolution equations of the form: u'(t)=A(t)u(t)+f(t,u(t)), t∈ℝ where (A(t))t∈ ℝ is a family of closed densely defined operators acting on a Banach space X that generates a strongly continuous evolution family which has an exponential dichotomy on ℝ. The nonlinear term f: ℝ × X \longrightarrow X is just μ-pseudo almost automorphic in Stepanov sense in t and Lipshitzian with respect to the second variable. For illustration, an application is provided for a class of nonautonomous reaction diffusion equations on ℝ.