Shocks and free boundaries: the local behaviour

Article type: Research Article

Authors: Kersner, R. | Natalini, R. | Tesei, A.

Affiliations: Computer and Automation Research Institute, Hungarian Academy of Sciences, P.O. Box 63, H-1518 Budapest, Hungary | Istituto per le Applicazioni del Calcolo “M. Picone”, Consiglio Nazionale della Ricerche, Roma, Italy | Dipartimento Matematico “G. Castelnuovo”, Università di Roma “La Sapienza”, Roma, Italy

Abstract: We study the Cauchy problem both for a non-linear diffusion-convection equation and for a first order hyperbolic conservation law. The latter can be regarded as the zero diffusion limit of the former, which is of degenerate parabolic type. Concerning support properties, the behaviour of solutions of both problems exhibits striking analogies when the effect of convection is stronger than diffusion. Hence previously reported phenomena concerning the parabolic problem can be interpreted as being of hyperbolic type.

DOI: 10.3233/ASY-1995-10105

Journal: Asymptotic Analysis, vol. 10, no. 1, pp. 77-93, 1995