tailieunhanh - Báo cáo hóa học: " Research Article Strong Stability and Asymptotical Almost Periodicity of Volterra Equations in Banach Spaces"

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 Strong Stability and Asymptotical Almost Periodicity of Volterra Equations in Banach Spaces | Hindawi Publishing Corporation Advances in Difference Equations Volume 2011 Article ID 414906 12 pages doi 2011 414906 Research Article Strong Stability and Asymptotical Almost Periodicity of Volterra Equations in Banach Spaces Jian-Hua Chen1 and Ti-Jun Xiao2 1 School of Mathematical and Computational Science Hunan University of Science and Technology Xiangtan Hunan 411201 China 2 School of Mathematical Sciences Fudan University Shanghai 200433 China Correspondence should be addressed to Ti-Jun Xiao xiaotj@ Received 1 January 2011 Accepted 1 March 2011 Academic Editor Toka Diagana Copyright 2011 . Chen and . Xiao. 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 study strong stability and asymptotical almost periodicity of solutions to abstract Volterra equations in Banach spaces. Relevant criteria are established and examples are given to illustrate our results. 1. Introduction Owing to the memory behavior cf. . 1 2 of materials many practical problems in engineering related to viscoelasticity or thermoviscoelasticity can be reduced to the following Volterra equation u T Au t f a t - s Au s ds t 0 0 u 0 x in a Banach space X with A being the infinitesimal generator of a Co-semigroup T t defined on X and a - e Lp R C a scalar function R 0 to and 1 p to which is often called kernel function or memory kernel cf. . 1 . It is known that the above equation is well-posed. This implies the existence of the resolvent operator S t and the mild solution is then given by u f S t x t 0 2 Advances in Difference Equations which is actually a classical solution if x e D A . In the present paper we investigate strong stability and asymptotical almost periodicity of the solutions. For more information and related topics about the two concepts we refer to the monographs 3 4 . In .

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