Year 2021, Volume 50 , Issue 3, Pages 692 - 698 2021-06-07

Continuous dependence of solutions to double dispersive equation with dissipative term

Mesude Elif UYSAL [1] , Şevket GÜR [2]


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.
structural stability, double dispersive equations, continuous dependence
  • [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.
Primary Language en
Subjects Mathematics
Journal Section Mathematics
Authors

Orcid: 0000-0003-0307-5174
Author: Mesude Elif UYSAL (Primary Author)
Institution: SAKARYA UNIVERSITY
Country: Turkey


Orcid: 0000-0002-7180-5952
Author: Şevket GÜR
Institution: SAKARYA UNIVERSITY
Country: Turkey


Dates

Publication Date : June 7, 2021

Bibtex @research article { hujms590313, journal = {Hacettepe Journal of Mathematics and Statistics}, issn = {2651-477X}, eissn = {2651-477X}, address = {}, publisher = {Hacettepe University}, year = {2021}, volume = {50}, pages = {692 - 698}, doi = {10.15672/hujms.590313}, title = {Continuous dependence of solutions to double dispersive equation with dissipative term}, key = {cite}, author = {Uysal, Mesude Elif and Gür, Şevket} }
APA Uysal, M , Gür, Ş . (2021). Continuous dependence of solutions to double dispersive equation with dissipative term . Hacettepe Journal of Mathematics and Statistics , 50 (3) , 692-698 . DOI: 10.15672/hujms.590313
MLA Uysal, M , Gür, Ş . "Continuous dependence of solutions to double dispersive equation with dissipative term" . Hacettepe Journal of Mathematics and Statistics 50 (2021 ): 692-698 <https://dergipark.org.tr/en/pub/hujms/issue/62731/590313>
Chicago Uysal, M , Gür, Ş . "Continuous dependence of solutions to double dispersive equation with dissipative term". Hacettepe Journal of Mathematics and Statistics 50 (2021 ): 692-698
RIS TY - JOUR T1 - Continuous dependence of solutions to double dispersive equation with dissipative term AU - Mesude Elif Uysal , Şevket Gür Y1 - 2021 PY - 2021 N1 - doi: 10.15672/hujms.590313 DO - 10.15672/hujms.590313 T2 - Hacettepe Journal of Mathematics and Statistics JF - Journal JO - JOR SP - 692 EP - 698 VL - 50 IS - 3 SN - 2651-477X-2651-477X M3 - doi: 10.15672/hujms.590313 UR - https://doi.org/10.15672/hujms.590313 Y2 - 2020 ER -
EndNote %0 Hacettepe Journal of Mathematics and Statistics Continuous dependence of solutions to double dispersive equation with dissipative term %A Mesude Elif Uysal , Şevket Gür %T Continuous dependence of solutions to double dispersive equation with dissipative term %D 2021 %J Hacettepe Journal of Mathematics and Statistics %P 2651-477X-2651-477X %V 50 %N 3 %R doi: 10.15672/hujms.590313 %U 10.15672/hujms.590313
ISNAD Uysal, Mesude Elif , Gür, Şevket . "Continuous dependence of solutions to double dispersive equation with dissipative term". Hacettepe Journal of Mathematics and Statistics 50 / 3 (June 2021): 692-698 . https://doi.org/10.15672/hujms.590313
AMA Uysal M , Gür Ş . Continuous dependence of solutions to double dispersive equation with dissipative term. Hacettepe Journal of Mathematics and Statistics. 2021; 50(3): 692-698.
Vancouver Uysal M , Gür Ş . Continuous dependence of solutions to double dispersive equation with dissipative term. Hacettepe Journal of Mathematics and Statistics. 2021; 50(3): 692-698.
IEEE M. Uysal and Ş. Gür , "Continuous dependence of solutions to double dispersive equation with dissipative term", Hacettepe Journal of Mathematics and Statistics, vol. 50, no. 3, pp. 692-698, Jun. 2021, doi:10.15672/hujms.590313