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Journals / Hacettepe Journal of Mathematics and Statistics / 2026 / Volume: 50 Issue: 3

Continuous dependence of solutions to double dispersive equation with dissipative term

Mesude Elif Uysal(SAKARYA UNIVERSITY)0000-0003-0307-5174
Şevket Gür(SAKARYA UNIVERSITY)0000-0002-7180-5952
Pages
—
Publication Date
2021-06-07
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

It is established that the solution depends continuously on the dispersive and dissipative coefficients.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:This work is focused on the properties of solutions to the initial-boundary value problem of the double dispersive-dissipative equation.
📊
Key Findings & Data:This work is focused on the properties of solutions to the initial-boundary value problem of the double dispersive-dissipative equation.
💡
Conclusion & Impact:It is established that the solution depends continuously on the dispersive and dissipative coefficients.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:structural stability · double dispersive equations · continuous dependence

Abstract

This work is focused on the properties of solutions to the initial-boundary value problem of the double dispersive-dissipative equation. It is established that the solution depends continuously on the dispersive and dissipative coefficients.

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Cite This Article

Uysal, M. E., Gür, Ş. (2021). Continuous dependence of solutions to double dispersive equation with dissipative term. Hacettepe Journal of Mathematics and Statistics, Volume: 50 Issue: 3. https://doi.org/10.15672/hujms.590313

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References (19)

  1. K.A. Ames and B. Straughan, Non-Standard and improperly posed problems, Mathematics in Science and Engineering Series, Academic Press, New York, 194, 1997.
  2. N. Bellomo and L. Preziosi, Modelling mathematical methods and scientific computation, CRC, Boca Raton, 1995.
  3. G. Chen, Y. Wang and S. Wang, Initial boundary value problem of the generalized cubic double dispersion equation, J. Math. Anal. Appl. 299 (2), 563-577, 2004.
  4. A.O. Çelebi, Ş. Gür and V.K. Kalantarov, Structural stability and decay estimate for marine riser equations, Math. Comput. Model. 54 (11-12), 3182-3188, 2011.
  5. A.O. Çelebi and V.K. Kalantarov, Decay of solutions and structural stability for the coupled Kuramoto-Sivashinsky-Ginzburg-Landau equations, Appl. Anal. 94 (11), 2342- 2354, 2015.
  6. H.F. Di and Y.D. Shang, Global existence and asymptotic behavior of solutions for the double dispersive-dissipative wave equation with nonlinear damping and source terms, Bound. Value Probl. 2015, Article No: 29, 2015.
  7. H.F. Di and Y.D. Shang, Cauchy Problem for a higher order generalized Boussinesqtype equation with hydrodynamical damped term, Appl. Anal. 95 (3), 690-714, 2016.
  8. H.F. Di and Y.D. Shang, Blow-Up Phenomena for a class of Generalized Double Dispersive Equations, Acta Math. Acad. Sci. 39 (2), 567-579, 2019.
  9. V.V. Gursky and A.M. Samsonov, Symmetries and exact solutions to a nonlinear doubly dispersive equation with dissipation, Conference: Day on Diffraction 2001, Proceedings, International Seminar, 2001.
  10. Ş. Gür and I. Güleç, Continuous dependence of solutions to fourth-order nonlinear wave equation, Hacet. J. Math Stat. 45, 367-371, 2016.
  11. Ş. Gür and M.E. Uysal, Continuous dependence of solutions to strongly damped nonlinear Klein-Gordon Equation, Turkish J. Math. 42, 904-910, 2018.
  12. C. Lin and L.E. Payne, Continuous dependence on the Soret coefficient for double diffusive convection in Darcy flow, J. Math. Anal. Appl. 342, 311-325, 2008.
  13. L.E. Payne and B. Straughan, Convergence and continuous Dependence for the Brinkman-Forchheimer equations, Stud. Appl. Math. 102, 419-439, 1999.
  14. A.M. Samsonov, Nonlinear Strain Waves in Elastic Waveguides, in: Jeffrey A., Engelbrecht J. (eds) Nonlinear Waves in Solids. CISM Courses and Lectures (International Centre for Mechanical Sciences), 341, Springer, Vienna, 1994.
  15. A.M. Samsonov and E.V. Sokurinskaya, Energy Exchange Between Nonlinear Waves in Elastic Waveguides and External Media, Nonlinear Waves in Active Media, Research Reports in Physics, Springer, Heidelberg, 1989.
  16. S. Wang and G. Chen, Cauchy problem of the generalized double dispersion equation, Nonlinear Anal. 64 (1) 159-173, 2006.
  17. M. Waurick, On the continuous dependence on the coefficients of evolutionary equations, Habilitation thesis, TU Dresden, arXiv: 1606.07731, 2016.
  18. R. Xu, Y. Liu and T. Yu, Global existence of solution for Cauchy problem of multidimensional generalized double dispersion equations, Nonlinear Anal. 71 (10), 4977- 4983, 2009.
  19. M. Yaman and Ş. Gür, Continuous dependence for the damped nonlinear hyperbolic equation, Math. Comput. Appl. 16 (2), 437-442, 2011.