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

Authors

  • vutrongluong@gmail.com Vu Trong Luong
  • thanhtungcva2013@gmail.com Nguyen Thanh Tung

Abstract

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. Refs 15.

Downloads

Download data is not yet available.

References

1. Chen G., Russell D.L. A Mathematical Model for Linear Elastic Systems with Structural Damping // Quart. Appl. Math. 1981/1982. Vol. 39. P. 433-454.

2. Huang F. A Problem for Linear Elastic Systems with Structural Damping // Acta Math. Sci Sinic. 1986. Vol. 6. P. 107-113.

3. Huang F. On the Mathematical Model for Linear Elastic Systems with Analytic Damping // SIAM, J. Cont, Opt. 1988. Vol. 26. P. 714-724.

4. Fan H., Li Y., Chen P. Existence of Mild Solutions for the Elastic Systems with Structural Damping in Banach Spaces // Abstract and Applied Analysis. 2013. Vol. 2013. Artical ID 746893. P. 1-6.

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. 2014. Vol. 410. P. 316-322.

6. Fan H., Gao F. Asymptotic Stability of Solutions to Elastic Systems with Structural Damping // Electronic Journal of Differential Equations. 2014. Vol. 2014, N245. P. 1-9.

7. Byszewski L. Theorems about existence and uniqueness of solutions of a semi-linear evolution nonlocal Cauchy problem // J. Math. Anal. Appl. 1991. Vol. 162. P. 494-505.

8. Deng K. Exponetial decay of solutions of semilinear parabolic equations with nonlocal initial conditions // J. Math. Anal. Appl. 1993. Vol. 179. P. 630-637.

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. 1991. Vol. 40. P. 11-19.

10. Kamenskii M., Obukhovskii V., Zecca P. Condensing Multivalued Maps and Semilinear Differential Inclusions in Banach Spaces. Berlin; New York: Walter de Gruyter, 2001.

11. Ахмеров Р. Р., Каменский М.И., Потапов А. С., Родкина А. Е., Садовский Б.Н. Меры некомпактности и уплотняющие операторы. Новосибирск: Наука, 1986. 265 с.

12. Anh N. T., Ke T.D. Decay Integral Solutions for Neutral Fractional Differential Equations with Infinite Delays // Math. Meth. Appl. Sci. 2015. Vol. 38, N8. P. 1601-1622.

13. Apell J. Mearures of Noncompactness Condensing Operators and Fixed Points an Application-Oriented Survey // Fixed Point Theory. 2005. Vol. 6, N2. P. 157-229.

14. Vrabie I.I. C0-semigroups and applications. Amsterdam: North-Holland Publishing Co., 2003.

15. Engel K.J., Nagel R. One-Parameter Semigroups for Linear Evolutio Equations. New York: Springer-Verlag Inc., 2000.

Published

2020-08-20

How to Cite

Vu Trong Luong, vutrongluong@gmail.com, & Nguyen Thanh Tung, thanhtungcva2013@gmail.com. (2020). Decay mild solutions for elastic systems with structural damping involving nonlocal conditions. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 4(1), 87–103. Retrieved from https://math-mech-astr-journal.spbu.ru/article/view/8578

Issue

Section

Mathematics