Electron. J. Diff. Eqns., Vol. 2002(2002), No. 19, pp. 1-10.

Relaxation approximations and bounded variation estimates for some partial differential equations

Francisco Caicedo, Yunguang Lu, & Mauricio Sepulveda

Abstract:
In this paper, we introduce a new technique for studying solutions of bounded variation for some conservation laws of first order partial differential equations and for some degenerate parabolic equations in multi-dimensional space. The connection between these two types of equations is the vanishing relaxation method.

Submitted November 15, 2001. Published February 19, 2002.
Math Subject Classifications: 35B40, 35D10, 35K15, 35K65, 35L65.
Key Words: Degenerate parabolic equation, Hyperbolic conservation laws, Relaxation approximation.

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Francisco Caicedo
Departamento de Matematicas y Estadistica
Universidad Nacional de Colombia, Bogota, Colombia
e-mail: jcaicedo@matematicas.unal.edu.co

Yunguang Lu
Departamento de Matematicas y Estadistica
Universidad Nacional de Colombia, Bogota, Colombia
e-amil: yglu@matematicas.unal.edu.co

Mauricio Sepulveda
Departamento de Ingenieria Matematica
Facultad de Ciencias Fisicas y Matematicas
Universidad de Concepcion,
Casilla 160-C, Concepcion, Chile
e-mail: mauricio@ing-mat.udec.cl

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