Resolution of the Partial Differential Equations of the Hyperbolic type with source term through the D’Alembert- Green Method’s
DOI:
https://doi.org/10.17268/sel.mat.2017.02.08Keywords:
Partial differential equation of hyperbolic type with term source non homogeneous, D’Alembert’s formula, Green’sAbstract
In the present work, we study a non-homogeneous second-order partial hyperbolic differential equation, its canonical form, its resolution using D’Alembert’s formula and Green’s theorem. Only mixed initial conditions that are not homogeneous are required to solve this problem. There are several physical problems that lead to this type of mathematical model, so this technique of resolution contributes to the knowledge of finding explicit solutions of problems such as two-dimensional wave type. Within the results the explicit solution of three cases is generated:
regarding the homogeneity and non-homogeneity of the initial conditions and the term source, from the point of view of analytical solution for continuous functions.
References
Sixto Romero, Francisco J. Moreno, IsabelL M. Rodríguez, Introducción a las Ecuaciones en Derivadas Parciales. Servicio de Publicaciones, Universidad de Huelva, 2001. Printed in Spain.
Andrei D. Polyanin, Handbook of Linear Partial Differential Equations for Engineers and Scientists. Chapman & Hall/CRC, 2002.
Tijonov A., Samarsky A., Ecuaciones de la Física Matemática. Editorial MIR, Primera Edición. Moscú, 1972.
Rafael Iório Júnior, Valéria de Magalhaes Ió Rio, Ecuacoes Diferenciais Parciais: Uma Introducao. Instituto de Matemática Pura e Aplicada, 1988.
Lawrence C. Evans, Partial Differential Equations. American Mathematical Society. Providence, Rhode Island, 1997.
Published
How to Cite
Issue
Section
License
The authors who publish in this journal accept the following conditions:
1. The authors retain the copyright and assign to the journal the right of the first publication, with the work registered with the Creative Commons Attribution License,Atribución 4.0 Internacional (CC BY 4.0) which allows third parties to use what is published whenever they mention the authorship of the work And to the first publication in this magazine.
2. Authors may make other independent and additional contractual arrangements for non-exclusive distribution of the version of the article published in this journal (eg, include it in an institutional repository or publish it in a book) provided they clearly state that The paper was first published in this journal.
3. Authors are encouraged to publish their work on the Internet (for example, on institutional or personal pages) before and during the review and publication process, as it can lead to productive exchanges and to a greater and more rapid dissemination Of the published work.
