Revista Integración, temas de matemáticas.

Revista Integración, temas de matemáticas

Vol. 28 No. 2 (2010): Revista Integración, temas de matemáticas
Research and Innovation Articles

Variational formulation of partial differential equations

PDF (Español (España))
  • Luis J. Collantes,
  • Aníbal Coronel
Luis J. Collantes
Universidad Nacional Pedro Ruiz Gallo
Aníbal Coronel
Universidad del Bío-Bío

Published 2010-09-21

Keywords

  • Variational formulation,
  • weak solutions,
  • Lax-Milgram Lemma

How to Cite

Collantes, L. J., & Coronel, A. (2010). Variational formulation of partial differential equations. Revista Integración, Temas De matemáticas, 28(2), 133–152. Retrieved from https://revistas.uis.edu.co/index.php/revistaintegracion/article/view/2172

Abstract

This paper deals with the study of the variational method for partial differential equations concerning the existence, uniqueness and regularity of the solution. The aim of this work is to give a comprehensive description of the variational method, presenting examples from the simple second order linear elliptic partial differential equations to a most complex first order non-linear partial differential equation. Comments on the adaptability of this method to this kind of equations are given.

PDF (Español (España))

Downloads

Download data is not yet available.

References

[1] Brézis H., Análisis Funcional, Alianza Editorial, Madrid, 1984.

[2] Ciarlet P.G., The Finite Element Method for Elliptic Problems, North-Holland, Amsterdam, 1978.

[3] Evans L., Partial Differential Equations, American Mathematical Society, Rhode Island, 1998.

[4] Godlewski E. and Raviart P.A., Hyperbolic Systems of Conservation Laws, Mathematiques & Applications, France, 1991.

[5] Kružkov S.N., “First order quasilinear equations in several independent variables”, Math. USSR-Sb., 10 (1970), 217–243.

[6] Smoller J., Shock Waves and Reaction-Diffusion Equations, Springer-Verlag, New York, 1983.