Discrete Dynamics in Nature and Society
Volume 2008 (2008), Article ID 405092, 13 pages
doi:10.1155/2008/405092

Existence and uniqueness of pseudo almost automorphic mild solutions to some classes of partial hyperbolic evolution equations

Abstract

We will establish an existence and uniqueness theorem of pseudo almost automorphic mild solutions to the following partial hyperbolic evolution equation (d/dt)[u(t)+f(t,Bu(t))]=Au(t)+g(t,Cu(t)),  t∈ℝ, under some assumptions. To illustrate our abstract result, a concrete example is given.