A Note on Asymptotic Stability of Semilinear Thermoelastic System

• Ajeet Singh ^[1] ; Velusamy Vijayakumar ^[2] ; Anurag Shukla ^[1] ; Saurabh Chauhan ^[1]
  1. [1] Rajkiya Engineering College Kannauj
  2. [2] Vellore Institute of Technology
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 21, Nº 3, 2022
• Idioma: inglés
• Enlaces
  • Texto completo (pdf)
• Resumen

  • In this article, our primary focus is on discussing the asymptotic stability of the semilinear thermoelastic system. Results are obtained with the help of contraction mapping. We assume the Lipschitz condition on the nonlinear term to get the main result.

• Referencias bibliográficas
  • 1. Sakthivel, R., Revathi, P., Ren, Y.: Existence of solutions for nonlinear fractional stochastic differential equations, Nonlinear. Analysis...
  • 2. Singh, A., Shukla, A.: Existence results for second-order semilinear stochastic delay differential equation, Mathematical Methods in the...
  • 3. Chadha, A., Bahuguna, D., Pandey, D.N.: Existence of a mild solution for a neutral stochastic fractional integro-differential inclusion...
  • 4. Bahuguna, D., Sakthivel, R., Chadha, A.: Asymptotic stability of fractional impulsive neutral stochastic partial integro-differential equations...
  • 5. Sakthivel, R., Ren, Y., Kim, H.: Asymptotic stability of second-order neutral stochastic differential equations. Journal of Mathematical...
  • 6. Sakthivel, R., Revathi, P., Mahmudov, N. I.: Asymptotic stability of fractional stochastic neutral differential equations with infinite...
  • 7. Sakthivel, R., Luo, J.: Asymptotic stability of nonlinear impulsive stochastic differential equations. Statistics and Probability Letters...
  • 8. Lu, Z., Zhu, Y., Xu, Q.: Asymptotic stability of fractional neutral stochastic systems with variable delays. European Journal of Control...
  • 9. Murad, S.A., Ameen, Z.A.: Existence and Ulam stability for fractional differential equations of mixed Caputo-Riemann derivatives. AIMS...
  • 10. Wang, X., Luo, D., Zhu, Q.: Ulam-Hyers stability of Caputo type fuzzy fractional differential equations with time-delays. Chaos, Solitons...
  • 11. Cheng, P., Lu, C., Cai, T.: Finite-time stability of impulsive stochastic delayed systems. Mathematical Methods in the Applied Sciences...
  • 12. Arthi, G., Brindha, N., Baleanu, D.: Finite-time stability results for fractional damped dynamical systems with time delays. Nonlinear...
  • 13. Shen, M., Fei, W., Mao, X., Deng, S.: Exponential stability of highly nonlinear neutral pantograph stochastic differential equations....
  • 14. Li, X., Song, S., Wu, J.: Exponential stability of nonlinear systems with delayed impulses and applications. IEEE Transactions on Automatic...
  • 15. Singh, A., Shukla, A., Vijayakumar, V., Udhayakumar, R.: Asymptotic stability of fractional order (1, 2] stochastic delay differential...
  • 16. Li, X., Yang, X.: Lyapunov stability analysis for nonlinear systems with state-dependent state delay, Automatica, 112 , 1-6. 108674 (2020)
  • 17. Li, X., Yang, X., Song, S.: Lyapunov conditions for finite-time stability of time-varying time-delay systems. Automatica 103, 135–140...
  • 18. Wei, Y., Cao, J., Chen, Y.,Wei, Y. : The proof of Lyapunov asymptotic stability theorems for Caputo fractional order systems. Applied...
  • 19. Avalos, G.: Exact controllability of a thermoelastic system with control in the thermal component only. Differential Integral Equations...
  • 20. Avalos, G., Lasiecka, I.: Exponential stability of a thermoelastic system with free boundary conditions without mechanical dissipation....
  • 21. Dell’Oro, F.: Asymptotic stability of thermoelastic systems of Bresse type. Journal of Differential Equations 258(11), 3902–3927 (2015)
  • 22. Rahmounea, A.: Existence and asymptotic stability for the semilinear wave equation with variableexponent nonlinearities. Journal of Mathematical...
  • 23. Qin, Y., Ren, J., Wei, T.: Global existence, asymptotic stability, and uniform attractors for nonautonomous thermoelastic systems with...
  • 24. Santos, M.L., Cordeiro, S.M.S., Maciel, E.S.: On the porous thermoelastic system with Coleman-Gurtin law. Applicable Analysis (2020)....
  • 25. Avalos, G., Lasiecka, I.: Exponential stability of a thermoelastic system with free boundary conditions without mechanical dissipation....
  • 26. Avalos, G., Lasiecka, I., Triggiani, R.: Uniform stability of Nonlinear thermoelastic plates with free boundary conditions, 13-32, International...
  • 27. Hoffmann, K. H., Leugering, G., Tröltzsch, F.: Optimal control of partial differential equations: international conference in Chemnitz,...