Decay mild solutions for elastic systems with structural damping involving nonlocal conditions

被引：15
作者：
Luong V.T. [1 ]
Tung N.T. [2 ]
机构：
[1] Department of Mathematics, Tay Bac University, Sonla
[2] Tay Bac University, 01, Chu Van An, Quyet Tam, Son La
来源：
Vestnik St. Petersburg University, Mathematics | 2017年 / 50卷 / 1期
关键词：
damping solutions; elastic system with structural damping; nonlocal conditions;
D O I：
10.3103/S1063454117010083
中图分类号：
学科分类号：
摘要：
This paper deals with a class of elastic systems with structural damping subject to nonlocal conditions. By using a suitable measure of noncompactness on the space of continuous functions on the half-line, we establish the existence of mild solutions with explicit decay rate of exponential type. An example is given to illustrate the abstract results. © 2017, Allerton Press, Inc.
引用
收藏
页码：55 / 67
页数：12
相关论文
共 15 条
  • [1] Chen G., Russell D.L., A mathematical model for linear elastic systems with structural damping, Q. Appl. Math., 39, pp. 433-454, (1981)
  • [2] Huang F., A problem for linear elastic systems with structural damping, Acta Math. Sci. Sin., 6, pp. 107-113, (1986)
  • [3] Huang F., On the mathematical model for linear elastic systems with analytic damping, SIAM J. Contol Opt., 26, pp. 714-724, (1988)
  • [4] Fan H., Li Y., Chen P., Existence of mild solutions for the elastic systems with structural damping in Banach spaces, Abs. Appl. Anal., 2013, pp. 1-6, (2013)
  • [5] Fan H., Li Y., Analyticity and exponential stability of semigroups for the elastic systems with structural damping in Banach spaces, J. Math. Anal. Appl., 410, pp. 316-322, (2014)
  • [6] Fan H., Gao F., Asymptotic stability of solutions to elastic systems with structural damping, Electron. J. Differ. Equations, 2014, 245, pp. 1-9, (2014)
  • [7] Byszewski L., Theorems about existence and uniqueness of solutions of a semi-linear evolution nonlocal Cauchy problem, J. Math. Anal. Appl., 162, pp. 494-505, (1991)
  • [8] Deng K., Exponetial decay of solutions of semilinear parabolic equations with nonlocal initial conditions, J. Math. Anal. Appl., 179, pp. 630-637, (1993)
  • [9] Byszewski L., Lakshmikantham V., Theorem about the existence and uniqueness of a solution of a nonlocal abstract Cauchy problem in a Banach space, Appl. Anal., 40, pp. 11-19, (1991)
  • [10] Kamenskii M., Obukhovskii V., Zecca P., Condensing Multivalued Maps and Semilinear Differential Inclusions in Banach Spaces, (2001)
12