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Afrika Matematika

, Volume 29, Issue 7–8, pp 1225–1235 | Cite as

Existence, stability and smoothness of bounded solutions for an impulsive semilinear system of parabolic equations

  • Hugo Leiva
  • Zoraida Sivoli
Article
  • 25 Downloads

Abstract

In this paper we study the existence, stability and smoothness of bounded solutions for an impulsive semilinear system of parabolic equations with homogeneous Dirichlet boundary condition. Using Banch fixed point theorem, we prove the existence of bounded solutions assuming that the nonlinear terms satisfy a Lipschitz condition, after that, we study the stability and the smoothness of such solutions.

Keywords

Impulsive semilinear system of parabolic equations Bounded solutions Stability, smoothness 

Mathematics Subject Classification

Primary 34K30 34k35 35R10 Secondary 93B05 93C10 

Notes

Acknowledgements

I want to thank the referees for their comments which helped to improve the presentation of this paper.

References

  1. 1.
    de Oliveira, L.A.: On reaction—diffusion systems. Electron. J. Differ. Equations 24, 1–10 (1998)MathSciNetGoogle Scholar
  2. 2.
    Diagana, T.: Well posedness for some damped elastic systems in Bancha spaces. Appl. Math Lett. 71, 74–80 (2017)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Fan, Z., Li, G.: Existence results for semilinear differential equations witn nonlocal and impulsive conditions. J. Funct. Anal. 258, 1709–1727 (2010)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Mallika Arjunan, M., Kavitha, V., Selvi, S.: Existence results for impulsive differential equations with nonlocal conditions via measure of noncompactness. J. Nonlinear Sci. Appl. 5, 195–205 (2012)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Jain, R.S., Dhakne, M.B.: On impulsive nonlocal integrodifferential equations with finite delay. Int. J. Math. Res. 5, 361–373 (2013)Google Scholar
  6. 6.
    Henry, D.: Geometric Theory of Semilinear Parabolic Equations. Springer, New York (1981)CrossRefGoogle Scholar
  7. 7.
    Leiva, H.: Stability of a periodic solution for a system of parabolic equations. J. Appl. Anal. 60, 277–300 (1996)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Leiva, H., Sequera, I.: Existence and stability of bounded solutions for a system of parabolic equations. J. Math. Anal. Appl. 279, 495–507 (2003)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Leiva, H., Sivoli, Z.: Existence, stability and smoothness of a bounded solutions for a nonlinear time varying thermoelastic plate equations. J. Math. Anal. Appl. 285, 191–211 (2003)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Leiva, H.: Existence of bounded solutions of a second order system with dissipation. J. Math. Anal. Appl. 237, 288–302 (1999)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Leiva, H.: Existence of bounded solutions of a second order evolution equation and applications. J. Math. Phys. 42, 945–952 (2001)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Leiva, H., Sundar, P.: Existence of solutions for a class of semilinear evolution equations whit impulses and delays. J. Nonlinear Evol. Equations Appl. 2017(7), 95–108 (2017) (ISSN: 2161-3680)Google Scholar
  13. 13.
    Lopez-Gomez, J., San Gil, R.P.: Coexistence in a simple food chain with diffusion. J. Math. Biol. 30, 655–668 (1992)Google Scholar

Copyright information

© African Mathematical Union and Springer-Verlag GmbH Deutschland, ein Teil von Springer Nature 2018

Authors and Affiliations

  1. 1.School of Mathematical Sciences and Information TechnologyYachay Tech UniversitySan Miguel de UrcuquiEcuador
  2. 2.Universidad de Los Andes-VenezuelaMéridaVenezuela
  3. 3.Facultad de CienciasEscuela Superior Politecnica de ChimborazoRiobambaEcuador

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