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.
[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.
Year 2021,
Volume: 50 Issue: 3, 692 - 698, 07.06.2021
[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.
Uysal, M. E., & Gür, Ş. (2021). Continuous dependence of solutions to double dispersive equation with dissipative term. Hacettepe Journal of Mathematics and Statistics, 50(3), 692-698. https://doi.org/10.15672/hujms.590313
AMA
Uysal ME, Gür Ş. Continuous dependence of solutions to double dispersive equation with dissipative term. Hacettepe Journal of Mathematics and Statistics. June 2021;50(3):692-698. doi:10.15672/hujms.590313
Chicago
Uysal, Mesude Elif, and Şevket Gür. “Continuous Dependence of Solutions to Double Dispersive Equation With Dissipative Term”. Hacettepe Journal of Mathematics and Statistics 50, no. 3 (June 2021): 692-98. https://doi.org/10.15672/hujms.590313.
EndNote
Uysal ME, Gür Ş (June 1, 2021) Continuous dependence of solutions to double dispersive equation with dissipative term. Hacettepe Journal of Mathematics and Statistics 50 3 692–698.
IEEE
M. E. 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, 2021, doi: 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.
JAMA
Uysal ME, Gür Ş. Continuous dependence of solutions to double dispersive equation with dissipative term. Hacettepe Journal of Mathematics and Statistics. 2021;50:692–698.
MLA
Uysal, Mesude Elif and Şevket Gür. “Continuous Dependence of Solutions to Double Dispersive Equation With Dissipative Term”. Hacettepe Journal of Mathematics and Statistics, vol. 50, no. 3, 2021, pp. 692-8, doi:10.15672/hujms.590313.
Vancouver
Uysal ME, Gür Ş. Continuous dependence of solutions to double dispersive equation with dissipative term. Hacettepe Journal of Mathematics and Statistics. 2021;50(3):692-8.