Relaxation approximations and bounded variation estimates for some partial differential equations

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.

Keywords

• Degenerate parabolic equation
• Hyperbolic conservation laws
• Relaxation approximation.