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Relaxation approximations and bounded variation estimates for some partial differential equations. (English) Zbl 0999.35059

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
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