Almost Periodic Solutions for Hyperbolic Semilinear Evolution Equations
Md. Maqbul and D. Bahuguna
Department of Mathematics and Statistics, Indian Institute of Technology Kanpur, Kanpur - 208016, India
Received June 22, 2011
Accepted October 10, 2011
Communicated by Michael Ruzhansky
| Abstract. In this paper we study the existence of almost periodic solutions for the semilinear evolution equation du/dt = A u + f(.,u), t ∈ R, under the sectoriallity of A, a linear operator with not necessarily dense domain, in a Banach space X and σ(A) ∩ iR=∅ We use the contraction mapping principle to show the existence and uniqueness of an almost periodic solution in an intermediate space Xα, when the function f: R × Xα → X is Stepanov-almost periodic. | |
| Keywords: | Sectorial operator; analytic semigroup; hyperbolic semigroup; Stepanov-almost periodic; almost periodic. |
| 2010 Mathematics Subject Classification: 34G20, 47D06, 34C27, 34K14. | |