Cauchy problem for some fourth-order nonstrictly hyperbolic equations
https://doi.org/10.17586/2220-8054-2016-7-5-869-879
Abstract
We describe the analytic solution of the Cauchy problem for some fourth-order linear hyperbolic equations with constant coefficients in a half-plane in the case of two independent variables, assuming certain conditions for the coefficients. Suitable conditions are assumed for the coefficients, and the equation operator is composed of first-order linear operators.
About the Authors
V. I. Korzyuk
Institute of Mathematics, Belarusian Academy of Sciences, Belarusian State University
Belarus
Belarus
N. V. Vinh
Institute of Mathematics, Belarusian Academy of Sciences, Belarusian State University
Belarus
Belarus
References
1. Korzyuk V.I., Kozlovskaya I.S. Solution of the Cauchy Problem for a Hyperbolic Equation with Constant Coefficients in the Case of Two Independent Variables. Differential Equations, 2012, 48 (5), P. 700–709.
2. Korzyuk V.I., Kozlovskaya I.S. Solution of the Cauchy Problem for a Hyperbolic Equation for a Homogeneous Differential Operator in the Case of Two Independent Variables. Dokl. NAN Belarusi, 2011, 55 (5), P. 9–13.
3. Petrovskii I.G. On the Cauchy Problem for Systems of Linear Partial Differential Equations in a Domain of Non analytic Functions. Bull. Moskov. Univ. Mat. Mekh., 1938, 1 (7), P. 1–72.
4. Korzyuk V.I. Equations of Mathematical Physics: lectures. Volume 4. Minsk, 2008 [in Russian].
5. Korzyuk V.I., Kozlovskaya I.S. Cauchy Problem for a Hyperbolic Equation with Constant Coefficients in the Case of Two Independent Variables. Mathematical Modeling and Differential Equations: Proc. 3rd Int. Sci. Conf., September 17?-22, 2012, Brest-?Minsk, 2012, P. 171–176.
6. Korzyuk V.I., Kozlouskaya I.S., Kozlov A.I. Caushy Problem in Half-Plane for Hyperbolic Equation with Constant Coefficients. In Analytic Methods of Analysis and Differential Equations (AMADE 2012), Cambridge, 2013, P. 45–71.
7. Gopalakrishnan S., Narendar S. Wave Propagation in Nanostructures. Springer International Publishing Switzerland, 2013.
8. Jalilir N. Piezoelectric-Based Vibration Control-From Macro to Micro/Nano Scale Systems. Springer Science + Business Media, LLC, 2010.
9. Doyle J.F. Wave propagation in structures. Springer, New York, 1999.
10. Gopalakrishnan S., Mitra M. Wavelet Methods for Dynamical Problems With Application to Metallic, Composite, and Nano-Composite Structures. Taylor and Francis Group, LLC, 2010
Review
For citations:
Korzyuk V.I., Vinh N.V. Cauchy problem for some fourth-order nonstrictly hyperbolic equations. Nanosystems: Physics, Chemistry, Mathematics. 2016;7(5):869-879. https://doi.org/10.17586/2220-8054-2016-7-5-869-879
Views:
4
Email this article 