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 Solutions for the Heat Equation with Sp -Pseudo Almost Automorphic Coefficients | Hindawi Publishing Corporation Boundary Value Problems Volume 2009 Article ID 182527 19 pages doi 2009 182527 Research Article Existence of Pseudo Almost Automorphic Solutions for the Heat Equation with Sp-Pseudo Almost Automorphic Coefficients Toka Diagana1 and Ravi P. Agarwal2 1 Department of Mathematics Howard University 2441 6th Street NW Washington DC 20005 USA 2 Department of Mathematical Sciences Florida Institute of Technology Melbourne FL 32901 USA Correspondence should be addressed to Ravi P. Agarwal agarwal@ Received 12 March 2009 Accepted 3 July 2009 Recommended by Veli Shakhmurov We obtain the existence of pseudo almost automorphic solutions to the N-dimensional heat equation with Sp-pseudo almost automorphic coefficients. Copyright 2009 T. Diagana and R. P. Agarwal. 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. 1. Introduction Let Q c Rn N 1 be an open bounded subset with C2 boundary ÔQ and let X L2 Q be the space square integrable functions equipped with its natural II L2 Q topology. Of concern is the study of pseudo almost automorphic solutions to the N-dimensional heat equation with divergence terms d L fCBw I Aw G t Bw t e R x e Q ot y t x 0 t e R x e dQ where the symbols B and A stand respectively for the first- and second-order differential operators defined by B Nd M dxj A ÌẾ dx and the coefficients F G R X Hj Q L2 Q are Sp-pseudo almost automorphic. 2 Boundary Value Problems To analyze our strategy will consist of studying the existence of pseudo almost automorphic solutions to the class of partial hyperbolic differential equations dt u t f t Bu t Au t g t Cu t t e R where A D A c X X is a sectorial linear operator on a Banach space X whose corresponding analytic semigroup T t t 0 is hyperbolic that is ơ A n iR 0 the operator B C are arbitrary linear
