On Burgers-type equations with nonmonotonic dissipative fluxes

Alexander Kurganov*, Doron Levy, Philip Rosenau

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We study a formation of patterns in Burgers-type equations endowed with a bounded but nonmonotonic dissipative flux: ut + f(u)x = ±vQ(ux)x, Q(s) = s/(1 + s2). Issues of uniqueness, existence, and smoothness of a solution are addressed. Asymptotic regions of a solution are discussed; in particular, classical and nonclassical traveling waves with an embedded subshock are constructed.

Original languageEnglish
Pages (from-to)443-473
Number of pages31
JournalCommunications on Pure and Applied Mathematics
Issue number5
StatePublished - May 1998


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