Welcome to Open Science
Contact Us
Home Books Journals Submission Open Science Join Us News
On a Singularly Perturbed System of First-Order Partial Differential Equations
Current Issue
Volume 3, 2015
Issue 3 (June)
Pages: 58-65   |   Vol. 3, No. 3, June 2015   |   Follow on         
Paper in PDF Downloads: 32   Since Aug. 28, 2015 Views: 2386   Since Aug. 28, 2015
Oksana Flyud, Department of Mathematical Economics and Econometrics, Faculty of Mechanics and Mathematics, Ivan Franko National University of Lviv, Lviv, Ukraine.
The initial boundary value problem for a system of singularly perturbed linear partial differential equations of the first order in the plane is considered, the small parameter is a multiplier for various partial derivatives. Constructed and proved asymptotic expansion of the first order solution with the powers of a small parameter.
Hyperbolic System, Boundary Value Problem, Singular Perturbed, Asymptotic Expansions, Boundary Layer Function
V Abolinya and A Myshkis. A mixed problem for linear hyperbolic system on the plane. Uchionye Zap. Latviisk. Univ., 20:87–104, 1958.
V. Butuzov and E. Derkunova. On a singularly perturbed system of first-order partial diferential equations with various degrees of a small parameter. Differential Equations, 42(6):826–841, 2006.
V. Butuzov and A. Karashchuk. On a singularly perturbed system of equations in the first partial derivatives. Math. Notes, 57, 1995.
P. Kordulova. Quasilinear hyperbolic equations with hysteresis. J. of Physics: Conference Series, 55:135–143, 2006.
O. Maulenov and A. Myshkis. On the solvability of a mixed problem for degenerate semilinear hyperbolic system on the interval. Math. Of the Kazakh SSR. Ser.fiz.-mat., 5:25–29, 1981.
A. Vasil’eva and V. Butuzov. Asymptotic methods in the theory of singular perturbations. Graduate School, Moscow, Russia, 1990.
Z. Wang. Exact controllability for nonautonomous first order quasilinear hyperbolic systems. Chin. Ann. Math., 27B(6), 2006.
S. Gui X. Chien and A. Friedman. A hyperbolic free boundary problem modeling tumor growth: asymptotic behavior. Trans. Amer. Math. Soc., 357(12), 2005.
Open Science Scholarly Journals
Open Science is a peer-reviewed platform, the journals of which cover a wide range of academic disciplines and serve the world's research and scholarly communities. Upon acceptance, Open Science Journals will be immediately and permanently free for everyone to read and download.
Office Address:
228 Park Ave., S#45956, New York, NY 10003
Phone: +(001)(347)535 0661
Copyright © 2013-, Open Science Publishers - All Rights Reserved