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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 840621, 14 pages
An Approximation of Ultra-Parabolic Equations
1Department of Mathematics, Fatih University, Istanbul, Turkey
2Department of Mathematics, ITTU, Ashgabat, Turkmenistan, Turkey
Received 7 February 2012; Accepted 3 April 2012
Academic Editor: Hasan Ali Yurtsever
Copyright © 2012 Allaberen Ashyralyev and Serhat Yılmaz. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- J. Dyson, E. Sanchez, R. Villella-Bressan, and G. F. Webb, “An age and spatially structured model of tumor invasion with haptotaxis,” Discrete and Continuous Dynamical Systems B, vol. 8, no. 1, pp. 45–60, 2007.
- K. Kunisch, W. Schappacher, and G. F. Webb, “Nonlinear age-dependent population dynamics with random diffusion,” Computers & Mathematics with Applications, vol. 11, no. 1–3, pp. 155–173, 1985, Hyperbolic partial differential equations, II.
- A. N. Kolmogorov, “Zur Theorie der stetigen zufälligen Prozesse,” Mathematische Annalen, vol. 108, pp. 149–160, 1933.
- A. N. Kolmogorov, “Zufällige Bewegungen,” Annals of Mathematics, vol. 35, pp. 116–117, 1934.
- T. G. Genčev, “On ultraparabolic equations,” Doklady Akademii Nauk SSSR, vol. 151, pp. 265–268, 1963.
- Q. Deng and T. G. Hallam, “An age structured population model in a spatially heterogeneous environment: existence and uniqueness theory,” Nonlinear Analysis, vol. 65, no. 2, pp. 379–394, 2006.
- G. di Blasio and L. Lamberti, “An initial-boundary value problem for age-dependent population diffusion,” SIAM Journal on Applied Mathematics, vol. 35, no. 3, pp. 593–615, 1978.
- G. di Blasio, “Nonlinear age-dependent population diffusion,” Journal of Mathematical Biology, vol. 8, no. 3, pp. 265–284, 1979.
- S. A. Tersenov, “Boundary value problems for a class of ultraparabolic equations and their applications,” Matematicheskiĭ Sbornik, vol. 133(175), no. 4, pp. 529–544, 1987.
- G. Akrivis, M. Crouzeix, and V. Thomée, “Numerical methods for ultraparabolic equations,” Calcolo, vol. 31, no. 3-4, pp. 179–190, 1994.
- A. Ashyralyev and S. Yılmaz, “On the approximate solution of ultra parabolic equations,” in Proceedings of the 2nd International Symposium on Computing in Science & Engineering, M. Güneş, A. K. Çınar, and I. Gürler, Eds., pp. 533––535, Gediz University, Izmir, Turkey, 2011.
- A. Ashyralyev and S. Yılmaz, “Second order of accuracy difference schemes for ultra parabolic equations,” AIP Conference Proceedings, vol. 1389, pp. 601–604, 2011.
- A. Ashyralyev and P. E. Sobolevskii, Well-Posedness of Parabolic Difference Equations Operator Theory Advance and Applications, vol. 69, Birkh äuser, Basel, Switzerland, 1994.
- P. E. Sobolevskii, “On the Crank-Nicolson difference scheme for parabolic equations,” Nonlinear Oscillations and Control Theory, pp. 98–106, 1978.
- A. A. Samarskii and E. S. Nikolaev, Numerical Methods for Grid Equations. Vol. 2: Iterative Methods, Birkhäuser, Basel, Switzerland, 1989.