tailieunhanh - báo cáo hóa học:" Research Article Existence of Pseudo-Almost Automorphic Mild Solutions to Some Nonautonomous Partial Evolution Equations"

Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Existence of Pseudo-Almost Automorphic Mild Solutions to Some Nonautonomous Partial Evolution Equations | Hindawi Publishing Corporation Advances in Difference Equations Volume 2011 Article ID 895079 23 pages doi 2011 895079 Research Article Existence of Pseudo-Almost Automorphic Mild Solutions to Some Nonautonomous Partial Evolution Equations Toka Diagana Department of Mathematics Howard University 2441 6th Street . Washington DC 20059 USA Correspondence should be addressed to Toka Diagana tokadiag@ Received 15 September 2010 Accepted 29 October 2010 Academic Editor Jin Liang Copyright 2011 Toka Diagana. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. We use the Krasnoselskii fixed point principle to obtain the existence of pseudo almost automorphic mild solutions to some classes of nonautonomous partial evolutions equations in a Banach space. 1. Introduction Let X be a Banach space. In the recent paper by Diagana 1 the existence of almost automorphic mild solutions to the nonautonomous abstract differential equations u f A f u f f t u ty t E R where A t for t E R is a family of closed linear operators with domains D A ty satisfying Acquistapace-Terreni conditions and the function f R X X X is almost automorphic in t E R uniformly in the second variable was studied. For that the author made extensive use of techniques utilized in 2 exponential dichotomy tools and the Schauder fixed point theorem. In this paper we study the existence of pseudo-almost automorphic mild solutions to the nonautonomous partial evolution equations d u t G t u t A t u t F t u tf t E R dt 2 Advances in Difference Equations where A f for t e R is a family of linear operators satisfying Acquistpace-Terreni conditions and F G are pseudo-almost automorphic functions. For that we make use of exponential dichotomy tools as well as the well-known Krasnoselskii fixed point principle to obtain some reasonable .