Solution of a Mixed Problem with Periodic Boundary Condition for a Quasi-Linear Euler-Bernoulli Equation

Year 2010, Volume: 39 Issue: 3, 417 - 428, 01.03.2010

H. Halilov K. Kutlu B.ö. Güler

Keywords

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References

• Chandrov, H. I. On Mixed Problem for A Class of Quasilinear Hyperbolic Equation (Tbilisi, 1970).
• Ciftci, I and Halilov, H. Fourier method for a quasilinear parabolic equation with periodic boundary condition, Hacettepe J. Math. Stat. 37 (2), 69–79, 2008.
• Ciftci, I and Halilov, H. Dependency of the solution of quasilinear pseudo-parabolic equation with periodic boundary condition, Int. J. Math. Anal. 2, 881–888, 2008.
• Conzalez-Valesco, E. A. Fourier Analysis and Boundary Value Problems (Academic Press, New York, 1995).
• Demir C., Akg¨oz B. and Civelek O. Free vibration and bending analysis of carbon nanotubes using Euler beam theory, Proceeding International Symp. on Engineering and Architectural Sciences of Balkan and Turkic Republics, Vol. III, 50–55, 2009.
• Elishakoff, I. and Candan, S. Apparently first closed-form solution for vibrating inhomoge- neous beams, Internat. J. Solids Structures 38 (19), 3411–3441, 2001.
• Gibson, R. F., Ayorinde, E. O. and Weng, Y. Vibration of carbon nano-tubes and their com- posites: A review, Compos Sci. Tech. 67, 1–28, 2007.
• Halilov, H. M. Solution of the mixed non-linear problem for a class of quasi-linear equation 4th order, J. Mathematical Physics and Functional Analysis, Alma Ata, 27–32, 1966.
• Halilov, H., On the Mixed Problem for a class of quasilinear pseudo-parabolic equations, Applicable Analysis 75 (1-2), 61–71, 2000.
• Halilov, H., Kutlu, K. and G¨uler, B. O. Investigation of the non-linear vibration problem, Proceedings of the Symposium on Engineering and Architectural Sciences of Balkan, Cauca- sus and Turkic Republics, Isparta, 79–84, 2009.
• Il’in, V. A. Solvability of mixed problem for hyperbolic and parabolic equations, Uspekhi Math. Nauk. 15-2 (92), 97–154, 1960 (in Russian).
• Ladyzhenskaya, D. A. Boundary Value Problem of Mathematical Physics (Springer, New York, 1985).
• Lattes R. and Lions, J.-L. Methode de Quasi-Reversibilit`e et Applications(Dunod, Paris, 1967).
• Shabadikov, K. H. Issledovanie Rashennie Smashannikh Zadach dlya Kvazilineaynikh Dif- ferentsialnikh Urevneniy Malim Parametrom pri Starshey SmessonoiPreizvodnoi(PhD The- sis, Fargana, 1984).
• Strutt, J. W. and Rayleigh B. The Theory of Sound (Dover Publication, New York, 1945).
• Wang, C. M., Tan, V. B. C. and Zhang, Y. Y. Timoshenko beam model for vibration analysis of multi-walled carbon nanotubes, J. Sound and Vibration 294, 1060–1072, 2006.