Continuous dependence of semilinear Petrovsky equation
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Authors
Hüseyin Kocaman
- Department of Mathematics, Sakarya University, Sakarya, Turkey.
Metin Yaman
- Department of Mathematics, Sakarya University, Sakarya, Turkey.
Şevket Gür
- Department of Mathematics, Sakarya University, Sakarya, Turkey.
Abstract
In this study, we obtain the continuous dependence on the coefficients of solutions of semilinear Petrovsky equation. Such
models are involved in various fields of mathematical physics likewise geophysical and oceanic applications.
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ISRP Style
Hüseyin Kocaman, Metin Yaman, Şevket Gür, Continuous dependence of semilinear Petrovsky equation, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 5, 2671--2677
AMA Style
Kocaman Hüseyin, Yaman Metin, Gür Şevket, Continuous dependence of semilinear Petrovsky equation. J. Nonlinear Sci. Appl. (2017); 10(5):2671--2677
Chicago/Turabian Style
Kocaman, Hüseyin, Yaman, Metin, Gür, Şevket. "Continuous dependence of semilinear Petrovsky equation." Journal of Nonlinear Sciences and Applications, 10, no. 5 (2017): 2671--2677
Keywords
- Semilinear Petrovsky equation
- continuous dependence.
MSC
References
-
[1]
G. N. Aliyeva, V. K. Kalantarov, Structural stability for FitzHugh-Nagumo equations, Appl. Comput. Math., 10 (2011), 289–293.
-
[2]
N. E. Amroun, A. Benaissa, Global existence and energy decay of solutions to a Petrovsky equation with general nonlinear dissipation and source term, Georgian Math. J., 13 (2006), 397–410.
-
[3]
A. O. Çelebi, V. K. Kalantarov, D. Uğurlu, Structural stability for the double diffusive convective Brinkman equations, Appl. Anal., 87 (2008), 933–942.
-
[4]
A.O. Çelebi, K. Gür, V. K. Kalantarov , Structural stability and decay estimate for marine riser equations, Math. Comput. Modelling, 54 (2011), 3182–3188.
-
[5]
J. Chen, Y. Jin, Continuous dependence on a parameter for classical solutions to first-order quasilinear hyperbolic systems, (Chinese) J. Fudan Univ. Nat. Sci., 39 (2000), 506–513.
-
[6]
W.-Y. Chen, Y. Zhou, Global nonexistence for a semilinear Petrovsky equation, Nonlinear Anal., 70 (2009), 3203–3208.
-
[7]
M. G. Coclite, A. Favini, G. R. Goldstein, J. A. Goldstein, S. Romanelli, Continuous dependence in hyperbolic problems with Wentzell boundary conditions, Commun. Pure Appl. Anal., 13 (2014), 419–433.
-
[8]
X.-S. Han, M.-X. Wang, Asymptotic behavior for Petrovsky equation with localized damping, Acta Appl. Math., 110 (2010), 1057–1076.
-
[9]
E. S. Huseynova, On behaviour of solution of Cauchy’s problem for one correct by Petrovsky equation at large time values, Trans. Natl. Acad. Sci. Azerb. Ser. Phys.-Tech. Math. Sci., Math. Mech., 26 (2006), 85–96.
-
[10]
B. A. Iskenderov, E. S. Huseynova, Estimation of the solution to Cauchy problem for a correct by Petrovsky equation, Trans. Natl. Acad. Sci. Azerb. Ser. Phys.-Tech. Math. Sci., Math. Mech., 29 (2009), 61–70.
-
[11]
G. Li, Y. Sun, W.-J. Liu, Global existence, uniform decay and blow-up of solutions for a system of Petrovsky equations, Nonlinear Anal., 74 (2011), 1523–1538.
-
[12]
A. V. Perjan, The continuous dependence of solutions of hyperbolic equations on initial data and coefficients, Studia Univ. Babeş-Bolyai Math., 37 (1992), 87–111.
-
[13]
F. Tahamtani, A. Peyravi, Global existence, uniform decay, and exponential growth of solutions for a system of viscoelastic Petrovsky equations, Turkish J. Math., 38 (2014), 87–109.
-
[14]
F. Tahamtani, M. Shahrouzi, Existence and blow up of solutions to a Petrovsky equation with memory and nonlinear source term, Bound. Value Probl., 2012 (2012), 15 pages.
-
[15]
M. Yaman, Ş. Gür, Continuous dependence for the damped nonlinear hyperbolic equation, Math. Comput. Appl., 16 (2011), 437–442.
-
[16]
Y. C. You, Energy decay and exact controllability for the Petrovsky equation in a bounded domain, Adv. in Appl. Math., 11 (1990), 372–388.
-
[17]
Y. C. You, Boundary stabilization of two-dimensional Petrovsky equation: vibrating plate, Differential Integral Equations, 4 (1991), 617–638.