Almost automorphic mild solutions of hyperbolic evolution equations with stepanov-like almost automorphic forcing term

• Main Authors: Indira Mishra, Dhirendra Bahuguna
• Format: Article
• Language: English
• Published: Texas State University 2012-11-01
• Series: Electronic Journal of Differential Equations
• Subjects: Almost automorphic; evolution equation; hyperbolic semigroups; extrapolation spaces; interpolation spaces; neutral differential equation; mild solution
• Online Access: http://ejde.math.txstate.edu/Volumes/2012/212/abstr.html

This article concerns the existence and uniqueness of almost automorphic solutions to the semilinear parabolic boundary differential equations $$displaylines{ x'(t)=A_mx(t)+f(t,x(t)), quad tin mathbb{R}, cr Lx(t)=phi(t,x(t)), quad tin mathbb{R}, }$$ where $A:=A_m|_{ker L}$ generates a hyperbolic analytic semigroup on a Banach space $X$, with Stepanov-like almost automorphic nonlinear term, defined on some extrapolated space $X_{alpha-1}$, for $0<alpha<1$ and $phi$ takes values in the boundary space $partial X$.