PDF
ZENODO
Published
2025-02-05
Section
Articles
How to Cite
How to Cite
THE CAUCHY PROBLEM FOR HYPERBOLIC TYPE EQUATIONS AND ITS SOLUTION BY THE METHOD OF CHARACTERISTICS.
Mirzagiyosova Sevinchbonu
Faculty of Physics and Mathematics, Mathematics Major, 1st year Master's student
Keywords: Cauchy problem, hyperbolic type equations, method of characteristics
Abstract
This article explores the Cauchy problem for hyperbolic type equations, focusing on the method of characteristics as a solution technique. The Cauchy problem is a fundamental problem in the theory of partial differential equations, where the goal is to find a solution that satisfies initial conditions given at a specific point in time. For hyperbolic type equations, the method of characteristics is a powerful tool for solving such problems. This method transforms the partial differential equation into a set of ordinary differential equations along certain curves, called characteristics, and provides an efficient way to derive the solution. The article delves into the theoretical foundations of the method, its applications, and discusses the advantages of using this approach for solving hyperbolic type equations. Practical examples and boundary conditions are also examined to illustrate the implementation of the method in various scenarios.
References
1. Courant, R., & Hilbert, D. (1989). Methods of Mathematical Physics: Volume I. Wiley-Interscience.
2. Evans, L. C. (2010). Partial Differential Equations (Graduate Studies in Mathematics). American Mathematical Society.
3. Lax, P. D. (2002). Hyperbolic Partial Differential Equations. SIAM.
4. Bressan, A. (2007). Hyperbolic Systems of Conservation Laws: The One-Dimensional Cauchy Problem. Oxford University Press.
5. Serre, D. (2000). Systèmes hyperboliques. Principes et méthodes. Presses Universitaires de France.
6. Ralston, J., & Rabinowitz, P. (2001). Introduction to the Theory of Linear Partial Differential Equations. Dover Publications.
7. Smoller, J. (1994). Shock Waves and Reaction-Diffusion Equations. Springer.
8. John, F. (1982). Partial Differential Equations (Fourth Edition). Springer.
9. Stoker, J. J. (1957). The Mathematical Theory of Linear Systems. Wiley.
10. Lax, P. D., & Wendroff, B. (1960). Systems of Conservation Laws. Communications on Pure and Applied Mathematics, 13(3), 217-237.
