Continuous dependence of a coupled system of Wave-Plate Type

Year 2017, Volume: 21 Issue: 6, 1389 - 1393, 01.12.2017

Yasemin Başcı , Şevket Gür

https://doi.org/10.16984/saufenbilder.319522

Abstract

In this study, we prove
continuous dependence of solutions on coefficients of a coupled system of
wave-plate type.

Keywords

wave-plate type, continuous dependence

Wave-Plate Tipi denklem sisteminin sürekli bağımlılığı

Abstract

Bu çalışmada, wave-plate tipi denklem sisteminin çözümlerinin
katsayılara sürekli bağımlılığı ispatlanmıştır.

Keywords

Wave-plate tipi, sürekli bağımlılık

References

• [1] K.A. Ames, L.E. Payne, “Continuous dependence results for solutions of the Navier-Stokes equations backward in time,” Nonlinear Anal. Theor. Math. Appl., 23, 103-113, 1994.
• [2] A.O. Çelebi, V.K. Kalantarov, D. Ugurlu, “On continuous dependence on coefficients of the Brinkman-Forchheimer equations,” Appl. Math. Lett., 19, 801-807, 2006
• [3] A.O. Çelebi, V.K. Kalantarov, D. Ugurlu, “Continuous dependence for the convective Brinkman-Forchheimer equations,” Appl. Anal. 84 (9), 877-888, 2005.
• [4] Changhao Lin, L.E. Payne, “Continuous dependence of heatux on spatial geometry for the generalized Maxwell-Cattaneosystem,” Z. Angew. Math. Phys. 55, 575-591, 2004.
• [5] F. Franchi, B. Straughan, “A continuous dependence on the body force for solutions to the Navier- Stokes equations and on the heat supply in a model for double-diffusive porous convection,” J. Math. Anal. Appl. 172, 117-129, 1993.
• [6] F. Franchi, B. Straughan, “Continuous dependence on the relaxation time and modelling, and unbounded growth,”J. Math. Anal. Appl. 185, 726-746, 1994.
• [7] F. Franchi, B. Straughan, “Spatial decay estimates and continuous dependence on modelling for an equation from dynamo theory,” Proc. R. Soc. Lond. A 445, 437-451, 1994.
• [8] F. Franchi, B. Straughan, “Continuous dependence and decay for the Forchheimer equations,” Proc. R. Soc. Lond. Ser. A 459,3195-3202, 2003.
• [9] Yan Li, C. Lin, “Continuous dependence for the nonhomogeneous Brinkman-Forchheimer equations in a semi-infnite pipe,” Appl. Mathematics and Computation 244, 201-208, 2014.
• [10] C. Lin, L.E. Payne, “Continuous dependence on the Soret coefficient for double diffusive convection in Darcy ow,” J. Math. Anal. Appl. 342 , 311-325, 2008.
• [11] Y. Liu, “Convergence and continuous dependence for the Brinkman-Forchheimer equations,” Math. Comput. Model. 49, 1401-1415, 2009.
• [12] Y. Liu, Y. Du, C.H. Lin, “Convergence and continuous dependence results for the Brinkman equations,” Appl. Math. Comput. 215 , 4443-4455, 2010.
• [13] L.E. Payne, J.C. Song and B. Straughan,“Continuous dependence and convergence results for Brinkman and Forchheimer models with variable viscosity,” Proc. R. Soc. Lond. A 45S , 2173-2190, 1999.
• [14] L.E. Payne, B. Straughan, “Convergence and continuous dependence for the Brinkman-Forchheimer equations,” Stud. Appl. Math. 102, 419-439, 1999.
• [15] M.L. Santos, J.E. Munoz Rivera, “Analytic property of a coupled system of wave-plate type with thermal effect,” Differential Integral Equations 24(9-10), 965-972, 2011.
• [16] N.L. Scott, “Continuous dependence on boundary reaction terms in a porous medium of Darcy type,” J. Math. Anal. Appl. 399, 667-675, 2013.
• [17] N.L. Scott, B. Straughan, “Continuous dependence on the reaction terms in porous convection with surface reactions,” Quart. Appl. Math. (in press).
• [18] B. Straughan, “The Energy Method, Stability and Nonlinear Convection,”Appl. Math. Sci. Ser., second ed., vol. 91, Springer, 2004.
• [19] B. Straughan, “Stability and Wave Motion in Porous Media,” Appl. Math. Sci. Ser., vol. 165, Springer, 2008.
• [20] B. Straughan, “Continuous dependence on the heat source in resonant porous penetrative convection,” Stud. Appl. Math. 127 , 302-314, 2011.
• [21] M. Yaman, Ş. Gür, “Continuous dependence for the pseudoparabolic equation,” Bound. Value Probl. , Art. ID 872572, 6 pp., 2010.
• [22] M. Yaman, Ş. Gür, “Continuous dependence for the damped nonlinear hyperbolic equation,” Math. Comput. Appl. 16 (2), 437-442, 2011.
• [23] G. Tang, Y. Liu, W. Liao, “Spatial behavior of a coupled systemof wave-plate type,” Abstract and Applied Analysisv volume 2014, Article ID 853693, 13 pages.
• [24] H. Tu, C. Lin,” Continuous dependence for the Brinkman equations of ow in double-diffusive convection,” Electron. J. Diff. Eq. 92 , 1-9, 2007.