Caicedo, Francisco; Lu, Yunguang; Supúlveda, Mauricio Relaxation approximations and bounded variation estimates for some partial differential equations. (English) Zbl 0999.35059 Electron. J. Differ. Equ. 2002, Paper No. 19, 10 p. (2002). Summary: 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 multidimensional space. The connection between these two types of equations is the vanishing relaxation method. MSC: 35L65 Hyperbolic conservation laws 35K65 Degenerate parabolic equations 35D10 Regularity of generalized solutions of PDE (MSC2000) 35K15 Initial value problems for second-order parabolic equations 35B25 Singular perturbations in context of PDEs Keywords:multidimensional space; vanishing relaxation method PDFBibTeX XMLCite \textit{F. Caicedo} et al., Electron. J. Differ. Equ. 2002, Paper No. 19, 10 p. (2002; Zbl 0999.35059) Full Text: EuDML EMIS