Resolution of the Partial Differential Equations of the Hyperbolic type with source term through the D’Alembert- Green Method’s

Authors

  • Irla Mantilla N. Facultad de Ciencias, Universidad Nacional de Ingeniería, Av. Túpac Amaru 210, Lima-Perú
  • Ysaac Suaña B. Facultad de Ciencias, Universidad Nacional de Ingeniería, Av. Túpac Amaru 210, Lima-Perú

DOI:

https://doi.org/10.17268/sel.mat.2017.02.08

Keywords:

Partial differential equation of hyperbolic type with term source non homogeneous, D’Alembert’s formula, Green’s

Abstract

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

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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

2017-12-15

How to Cite

N., I. M., & B., Y. S. (2017). Resolution of the Partial Differential Equations of the Hyperbolic type with source term through the D’Alembert- Green Method’s. Selecciones Matemáticas, 4(02), 211-219. https://doi.org/10.17268/sel.mat.2017.02.08