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On the critical behavior in nonlinear evolutionary PDEs with small viscocity

TitleOn the critical behavior in nonlinear evolutionary PDEs with small viscocity
Publication TypeJournal Article
Year of Publication2012
AuthorsDubrovin, B, Elaeva, M
JournalRussian Journal of Mathematical Physics. Volume 19, Issue 4, December 2012, Pages 449-460
Abstract

We address the problem of general dissipative regularization of the quasilinear transport equation. We argue that the local behavior of solutions to the regularized equation near the point of gradient catastrophe for the transport equation is described by the logarithmic derivative of the Pearcey function, a statement generalizing the result of A.M.Il\\\'in \\\\cite{ilin}. We provide some analytic arguments supporting such conjecture and test it numerically.

URLhttp://hdl.handle.net/1963/6465
DOI10.1134/S106192081204005X

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